There is a narration from 'A'isha that says that Holy Prophet (s) died with his head in her lap, however, according to narrations in Usul al-Kafi, Volume 1, and also other Sunni narrations, the Holy Prophet (s) died with his head in the lap of Imam 'Ali (as). Imam 'Ali narrates this, saying that the Holy Prophet (s) kept on whispering to him and passing on knowledge. He 'opened a thousand gates, each of which opened another thousand gates.' Someone later asked Imam al-Sadiq (as) how many of those gates had been opened to the Shi'a and Imam al-Sadiq (as) said, 'Not even two'. So, the final words were whispered to Imam 'Ali (as) and we don't know what they were.
“I laid you down in your grave when your last breath has passed between my neck and chest.” (Nahj al-Balagha, Sermon 201, p.441)
“When the Prophet (saas) died his head was on my chest, and his (last) breath blew over my palms and I passed it over my face.” (Nahj al-Balagha, Sermon 196, p.431)
The following is quoted in Khasa’is of Nasa’i from Umm Salamah: "By Allah, the closest person [to the Prophet] at the time of the Prophet's death was ‘Ali. Early on the morning of the day when he was going to die, the Prophet called ‘Ali who had been sent out on some errand. He asked for ‘Ali three times before his return. However, ‘Ali came before sunrise. So, thinking that the Prophet needed some privacy with ‘Ali, we came out. I was the last to be out; therefore, I sat closer to the door than the other women. I saw that ‘Ali lowered his head towards the Prophet and the Prophet kept whispering into his ears (for sometime). Therefore, ‘Ali is the only person who was near the Prophet till the last."
Al-Hakim al-Nasyaburi, moreover, remarks in his Mustadrak that: "the Prophet kept confiding in ‘Ali till the time of his death. Then he breathed his last."
Imam al-Sadiq (as) narrates: ‘The Messenger of Allah (p.b.u.h.a.h.p.) said in his illness duringwhich he died: “Call to me my sincere friend (khalq).” And the two women (‘A’isha and Hafsa) sent for their fathers, and, when the Messenger of Allah (p.b.u.h.a.h.p.) saw them, he turned away from them. Then he said: “Call to me my sincere friend.” So ‘Ali was sent for, and when he saw him, he (‘Ali - p.b.u.h.) bent over him and (the Prophet - p.b.u.h.a.h.p.) spoke to him. When he came out, the two (fathers) met him (‘Ali - p.b.u.h.) and said to him: “What did your sincere friend say to you?” He said: “He spoke to me about a thousand gates, each one of which opens (the way to another) thousand gates.”’ (Al-Kulaynī, al-Kāfi, Vol. 1, al-Usūl, Part Two, 4: ‘The Book of Divine Proof’, Chapter 65 ‘The Sign and the Warrant for Amir al-Mu’minin Peace Be Upon Him’, no. 767-4, p. 375.)