I heard Allah's Messenger (ﷺ) say, and he then narrated (the above-mentioned hadith).
Sahih Muslim Book 33, Hadith 12
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I wrote (a letter) to Jabir b. Samura and sent it to him through my servant Nafi', asking him to inform me of something he had heard from the Messenger of Allah (ﷺ). He wrote to me (in reply): I heard the Messenger of Allah (ﷺ) say on Friday evening, the day on which al-Aslami was stoned to death (for committing adultery): The Islamic religion will continue until the Hour has been established, or you have been ruled over by twelve Caliphs, all of them being from the Quraish. also heard him say: A small force of the Muslims will capture the white palace, the police of the Persian Emperor or his descendants. I also heard him say: Before the Day of Judgment there will appear (a number of) impostors. You are to guard against them. I also heard him say: When God grants wealth to any one of you, he should first spend it on himself and his family (and then give it in charity to the poor). I heard him (also) say: I will be your forerunner at the Cistern (expecting your arrival).
Sahih Muslim Book 33, Hadith 11 Next Hadith → I was present with my father when he was wounded. People praised him and said: May God give you a noble recompense! He said: I am hopeful (of God's mercy) as well as afraid (of His wrath) People said: Appoint anyone as your successor. He said: Should I carry the burden of conducting your affairs in my life as well as in my death? (So far as Caliphate is concerned) I wish I could acquit myself (before the Almighty) in a way that there is neither anything to my credit nor anything to my discredit. If I would appoint my successor, (I would because) one better than me did so. (He meant Abu Bakr.) If I would leave You alone, (I would do so because) one better than me, i. e. the Messenger of Allah (ﷺ), did so. 'Abdullah says: When he mentioned the Messenger of Allah (ﷺ) I understood that he would not appoint anyone as Caliph.
Sahih Muslim Book 33, Hadith 13
Sahih Muslim Book 33, Hadith 11 Next Hadith → I was present with my father when he was wounded. People praised him and said: May God give you a noble recompense! He said: I am hopeful (of God's mercy) as well as afraid (of His wrath) People said: Appoint anyone as your successor. He said: Should I carry the burden of conducting your affairs in my life as well as in my death? (So far as Caliphate is concerned) I wish I could acquit myself (before the Almighty) in a way that there is neither anything to my credit nor anything to my discredit. If I would appoint my successor, (I would because) one better than me did so. (He meant Abu Bakr.) If I would leave You alone, (I would do so because) one better than me, i. e. the Messenger of Allah (ﷺ), did so. 'Abdullah says: When he mentioned the Messenger of Allah (ﷺ) I understood that he would not appoint anyone as Caliph.
Sahih Muslim Book 33, Hadith 13