Abdullah bin Umar reported,

I entered upon Hafsah, and she said, "Are you aware that your father does not intend to appoint a successor?"I said, "He would not do that."She said, "He is going to do it."So I swore that I would speak to him about it. Then I kept silent, and morning came without my having spoken to him. It felt as though I were carrying a mountain in my right hand until I returned.I entered upon him, and he asked me about the condition of the people, and I informed him. Then I said to him, "I heard the people saying something, and I made an oath that I would say it to you. They claim that you do not intend to appoint a successor. If you had a shepherd in charge of camels or sheep, and he came to you having abandoned them, you would consider that he had failed in his duty. The shepherding of people is even weightier."My words struck him. He lowered his head for a while, then raised it toward me and said, "Allah will safeguard His religion. As for me, if I do not appoint a successor, the Messenger of Allah ﷺ did not appoint a successor, and if I do appoint a successor, then Abu Bakr did appoint a successor."By Allah, the moment he mentioned the Messenger of Allah ﷺ and Abu Bakr, I knew that he would never place anyone on a par with the Messenger of Allah ﷺ, and that he would not appoint a successor.

عن ابن عمر قال

دخلت على حفصة، فقالت: أعلمت أن أباك غير مستخلف؟ قال: قلت: ما كان ليفعل، قالت: إنه فاعل قال: فحلفت أني أكلمه في ذلك فسكت، حتى غدوت، ولم أكلمه قال: فكنت كأنما أحمل بيميني جبلا حتى رجعت، فدخلت عليه، فسألني عن حال الناس، وأنا أخبره قال: ثم قلت له: إني سمعت الناس يقولون مقالة، فآليت أن أقولها لك، زعموا أنك غير مستخلف، وإنه لو كان لك راعي إبل أو راعي غنم ثم جاءك وتركها، رأيت أن قد ضيع، فرعاية الناس أشد قال: فوافقه قولي، فوضع رأسه ساعة ثم رفعه إلي فقال: إن الله عز وجل يحفظ، وإني لئن لا أستخلف فإن رسول الله ﷺ لم يستخلف، وإن أستخلف فإن أبا بكر قد استخلف قال: فوالله ما هو إلا أن ذكر رسول الله ﷺ وأبا بكر فعلمت أنه لم يكن ليعدل برسول الله ﷺ أحدا، وأنه غيرمستخلف.