Narrated Al-Aswad:
In the presence of ‘Aisha some people mentioned that the Prophet had appointed ‘Ali by will as his successor. ‘Aisha said, “When did he appoint him by will? Verily when he died he was resting against my chest (or said: in my lap) and he asked for a wash-basin and then collapsed while in that state, and I could not even perceive that he had died, so when did he appoint him by will?”
Sahih Bukhari, Volume 4, Book51, Number 4