It has been reported on the authority of Ibn 'Umar who said

I entered the apartment of (my sister) Hafsa. She said: Do yoa know that your father is not going to nominate his successor? I said: He won't do that (i. e. he would nominate). She said: He is going to do that. The narrator said: I took an oath that I will talk to him about the matter. I kept quiet until the next morning, still I did not talk to him, and I felt as if I were carryint, a mountain on my right hand. At last I came to him and entered his apartment. (Seeing me) he began to ask me about the condition of the people, and I informed him (about them). Then I said to him: I heard something from the people and took an oath that I will communicate it to you. They presume that you are not going to nominate a successor. If a grazer of camels and sheep that you had appointed comes back to you leaving the cattle, you will (certainly) think that the cattle are lost. To look after the people is more serious and grave. (The dying Caliph) was moved at my words. He bent his head in a thoughtful mood for some time and raised it to me and said: Allah will doubtlessly protect His religion. If I do not nominate a successor (I have a precedent before me), for the Messenger of Allah (ﷺ) did not nominate his successor. And if I nominate one (I have a precedent), for Abu Bakr did nominate. The narrator (Ibn Umar) said: By Allah. when he mentioned the Messenger of Allah (ﷺ) and Abu Bakr, I (at once) understood that he would not place anyone at a par with the Messenger of Allah (ﷺ) and would not nominate anyone.