Sh. Saduq narrated in his “Ilal ush sharae” (p167):
The apostle of Allah SAWS said: “O ‘Abbas, do you accept to succeed me, implement my religion and fulfill my commitment?” al-‘Abbas said: “I am a man of old age, I have a big family and I have no money.” Then the Prophet SAWS repeated this to him three times but he rejected it. The Prophet SAWS then said: “I will give it to a man who deserves it and he shall not say what you say .” He said: “O ‘Ali, do you accept to succeed me, implement my religion and fulfill my commitment?” ‘Ali then felt as if he was being suffocated and couldn’t reply, then he saw the head of the Prophet SAWS going back and forth, the Prophet SAWS repeated his offer and ‘Ali replied: “Yes, may my mother and father be a sacrifice for you.”
As you can see stated that when prophet (sallalahu alaihi wa ala alihi wa sallam) was on his death bed, after SO CALLED APPOINTMENT IN GADIR, he asked Abbas if he want to accept his wasiyah!!!