Before passing away, Hazrat ‘Umar (radhiyallahu ‘anhu) did not appoint any specific person to succeed him as the Khalifah. Instead, when someone suggested to Hazrat ‘Umar (radhiyallahu ‘anhu) that he appoint the next Khalifah, he said, “If I do not appoint a Khalifah, then Rasulullah (sallallahu ‘alaihi wasallam) did not appoint a Khalifah, and if I appoint a Khalifah, then Hazrat Abu Bakr (radhiyallahu ‘anhu) had appointed a Khalifah.”
Hazrat ‘Abdullah bin ‘Umar (radhiyallahu ‘anhu) says, “By Allah! When I heard my father mention the example of Rasulullah (sallallahu ‘alaihi wasallam) and Hazrat Abu Bakr (radhiyallahu ‘anhu), then I knew that he would choose the example of Rasulullah (sallallahu ‘alaihi wasallam) and would not equate any one to Rasulullah (sallallahu ‘alaihi wasallam). Hence, I understood that he would not appoint a Khalifah.”
In one report, it is mentioned that Hazrat ‘Umar (radhiyallahu ‘anhu) replied in the following words:
“If I appoint a Khalifah, then the person who was before me and superior to me appointed a Khalifah (referring to Hazrat Abu Bakr Siddeeq (radhiyallahu ‘anhu)), and if I do not appoint a Khalifah, then there was someone before me who did not appoint a Khalifah (referring to Rasulullah (sallallahu ‘alaihi wasallam)).”
(Saheeh Muslim #567 and #1823)