Narrated Al-Aswad: It was mentioned in the presence of `Aisha that the Prophet (ﷺ) had appointed `Ali as successor by will. Thereupon she said, "Who said so? I saw the Prophet, while I was supporting him against my chest. He asked for a tray, and then fell on one side and expired, and I did not feel it. So how (do the people say) he appointed `Ali as his successor?"
Source: sunnah.com
Other translations
Arabic
حَدَّثَنَا عَبْدُ اللَّهِ بْنُ مُحَمَّدٍ، أَخْبَرَنَا أَزْهَرُ، أَخْبَرَنَا ابْنُ عَوْنٍ، عَنْ إِبْرَاهِيمَ، عَنِ الأَسْوَدِ، قَالَ ذُكِرَ عِنْدَ عَائِشَةَ أَنَّ النَّبِيَّ صلى الله عليه وسلم أَوْصَى إِلَى عَلِيٍّ، فَقَالَتْ مَنْ قَالَهُ لَقَدْ رَأَيْتُ النَّبِيَّ صلى الله عليه وسلم وَإِنِّي لَمُسْنِدَتُهُ إِلَى صَدْرِي، فَدَعَا بِالطَّسْتِ فَانْخَنَثَ فَمَاتَ، فَمَا شَعَرْتُ، فَكَيْفَ أَوْصَى إِلَى عَلِيٍّ
sunnah.com