Short answer
No. Muslims worship God (﷾) alone. Worshipping anyone beside Him, even the Prophet Muhammad (ﷺ), is the worst sin in Islam. The Qur'an tells him to say he has no power to help or harm even himself. He told his followers not to over-praise him as Christians praised Jesus. He asked to be called the servant of Allah (﷾) and His messenger. When he died, his closest friend Abu Bakr told the grieving crowd that whoever worshipped Muhammad (ﷺ) should know he was dead. Whoever worshipped Allah (﷾) should know that Allah (﷾) is alive and never dies. The old name "Muhammadans" was made up on the pattern of "Christians", as if Muslims treated him as Christians treat Jesus. Muslims love him and follow his example, but they pray only to God (﷾).
Full explanation
What the Qur'an says he was
The Qur'an tells the Prophet (ﷺ) to say that he has no power over good or harm, even for himself. It tells him to say that he is a man like other men, to whom a revelation came. It calls him a mercy sent to all creatures. He was sent, so he is a servant, not the one who sends.
“Say: "I have no power over any good or harm to myself except as Allah willeth. If I had knowledge of the unseen, I should have multiplied all good, and no evil should have touched me: I am but a warner, and a bringer of glad tidings to those who have faith."”
“Say: "I am but a man like yourselves, (but) the inspiration has come to me, that your Allah is one Allah: whoever expects to meet his Lord, let him work righteousness, and, in the worship of his Lord, admit no one as partner.”
“We sent thee not, but as a Mercy for all creatures.”
What he told his followers
The Prophet (ﷺ) named the danger himself. He told his followers not to over-praise him as Christians had over-praised the son of Mary. He told them to call him the servant of Allah (﷾) and His messenger. Once he prayed sitting down, and his followers stood behind him. He signalled them to sit. He told them they had nearly done what Persians and Romans do, standing while their kings sit.
Umar reports that he heard the Prophet (ﷺ) say: do not over-praise me as the Christians over-praised the son of Mary; I am only a servant, so call me the servant of Allah and His Messenger.
Jabir reports that the Prophet (ﷺ), when ill, led the prayer sitting, and the people behind him stood. He signalled them to sit, and afterwards told them they had nearly done what the Persians and Romans do, who stand before their kings while the kings sit, and that they must not do it.
The day he died
The real test came when the Prophet (ﷺ) died in 632. Umar, another close companion, was overcome and insisted he was not dead. Abu Bakr kissed the Prophet's (ﷺ) face. He went out to the people and said that whoever worshipped Muhammad (ﷺ) should know he was dead. Whoever worshipped Allah (﷾) should know that Allah (﷾) is alive. Then he recited the verse that says Muhammad (ﷺ) is no more than a messenger. A young community could have made its leader divine that day. Abu Bakr, soon to be the first caliph (leader of the Muslims), closed that door in one sentence. In fourteen centuries, Islam has never taught that he was divine.
Aisha reports that when the Prophet (ﷺ) died, Umar insisted he was not dead. Abu Bakr went in, uncovered his face and kissed him, then came out and told the people: whoever worshipped Muhammad, Muhammad is dead; whoever worshipped Allah, Allah is alive and never dies. He then recited Qur'an 39:30 and 3:144.
“Muhammad is no more than a messenger: many Were the messenger that passed away before him. If he died or were slain, will ye then Turn back on your heels? If any did turn back on his heels, not the least harm will he do to Allah; but Allah (on the other hand) will swiftly reward those who (serve Him) with gratitude.”
Why there are no pictures of him
The Islamic method forbids images of the Prophet (ﷺ), and of God (﷾), for the same reason. Ibn Abbas, the Prophet's (ﷺ) cousin and companion, reported how idols began among Noah's people. They began as statues of righteous men, set up after they died. They were worshipped only after those who made them had died and their origin was forgotten. The Prophet (ﷺ) cleared the idols from the Ka'ba, the House of God (﷾) in Mecca. Pictures of Abraham and Ishmael were among them. He also warned against image-making. The rule is the one Moses brought down the mountain in the Ten Commandments. It shows how carefully Islam guards against anyone worshipping its Prophet (ﷺ).
“(He is) the Creator of the heavens and the earth: He has made for you pairs from among yourselves, and pairs among cattle: by this means does He multiply you: there is nothing whatever like unto Him, and He is the One that hears and sees (all things).”
Ibn Abbas explains that the idols of Noah's people, Wadd, Suwa', Yaghuth, Ya'uq and Nasr, bore the names of righteous men. When those men died, their people set up statues where they used to sit and named the statues after them. The statues were not worshipped at first; only when that generation had died and the reason for them was forgotten did people begin to worship them.
Ibn Abbas reports that when the Prophet (ﷺ) came to Mecca he would not enter the Ka'ba while idols were in it, and ordered them taken out. Pictures of Abraham and Ishmael were among the things removed.
Abdullah ibn Mas'ud reports that the Prophet (ﷺ) said the makers of images will receive the severest punishment from Allah.
“Thou shalt have no other gods before me. Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth: Thou shalt not bow down thyself to them, nor serve them: for I the Lord thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me;”
What looks like worship, and what it is
Qur'an 33:56 — Surat al-Ahzab (The Clans), verse 56
“Allah and His angels send blessings on the Prophet: O ye that believe! Send ye blessings on him, and salute him with all respect.”
Cited for
Muslims call down blessings on Muhammad (ﷺ) in every prayer and whenever his name is spoken. So they seem to be praying to him.
The response
The verse tells believers to ask God (﷾) to bless him. The words Muslims say are a prayer to God (﷾) on the Prophet's (ﷺ) behalf: "O Allah, bless Muhammad." He is the one prayed for, not the one prayed to. In the same prayer every Muslim says to God (﷾), "Thee do we worship, and Thine aid we seek." In the sitting of the prayer, every Muslim also testifies that Muhammad (ﷺ) is God's (﷾) servant and Messenger.
Where it lands — Asking God (﷾) to bless someone is a prayer to God (﷾), not worship of that person.
Sahih al-Bukhari 15 — Kitab al-Iman (Book of Belief), hadith 15
Anas reports that the Prophet (ﷺ) said none of them has faith until he loves the Prophet more than his father, his children and all people.
Cited for
Muslims are told to love Muhammad (ﷺ) more than their parents, their children and everyone else. That is devotion that belongs only to God.
The response
Muslims love him because God (﷾) sent him, and that love shows in following him. Worship in Islam means prayer, prostration (bowing with the forehead on the ground), sacrifice and calling on someone for help that only God (﷾) can give. Every one of these goes to God (﷾) alone. The Prophet (ﷺ), who said Muslims must love him most, also forbade praise beyond his rank. He stopped people standing over him while he sat, as subjects stand before kings. He told them to call him a servant.
Where it lands — Loving the Prophet (ﷺ) above all people is not worshipping him; the same teaching forbids treating him as divine.
Perspectives
The Islamic perspective
Muhammad (ﷺ) was a human being chosen as God's (﷾) last messenger. Muslims love him, honour him and follow his example, and they worship God (﷾) alone. Worshipping him, or anyone else, alongside God (﷾) cancels a person's Islam.
The Qur'an commands the Prophet (ﷺ) to say he has no power over any good or harm to himself except as Allah (﷾) wills. It also has him say he has no knowledge of the unseen.
The Qur'an commands him to say that he is only a man like other people. It is revealed to him that God (﷾) is one.
The Prophet (ﷺ) forbade his followers to over-praise him as Christians over-praised Jesus. He told them to call him the servant of Allah (﷾) and His messenger.
He stopped his followers from standing behind him while he sat, as subjects stand before kings.
When he died, Abu Bakr told the community that Muhammad (ﷺ) was dead and only Allah (﷾) is alive. He recited that Muhammad (ﷺ) is no more than a messenger.
Setting up partners with God (﷾) is the one sin the Qur'an says God (﷾) does not forgive to one who dies on it unrepentant. So worshipping the Prophet (ﷺ) would be the gravest sin a Muslim could commit.
The Islamic method forbids images of the Prophet (ﷺ) so that he can never become an object of veneration. The Ten Commandments forbid graven images for the same reason.