Uthman suffered a severe nosebleed in the year of the nosebleed, so much so that he was unable to perform the Hajj, and he made his will. A man from Quraysh came in to see him and said, "Appoint a successor."Uthman asked, "Have they been speaking of this?"The man replied, "Yes."Uthman asked, "Whom do they name?"The man fell silent.Then another man entered and said the same thing to him, and Uthman gave him a similar response.Then Uthman
asked, "Did they name Zubayr?"The man said, "Yes."Uthman said, "By the One in whose hand my soul rests, he is indeed the best of them as far as I know, and the most beloved of them to the Messenger of Allah ﷺ."
حدثنا زكريا بن عدي حدثنا علي بن مسهر عن هشام بن عروة عن أبيه
أصاب عثمان رضي الله عنه رعاف سنة الرعاف حتى تخلف عن الحج وأوصى فدخل عليه رجل من قريش فقال استخلف قال وقالوه قال نعم قال من هو قال فسكت قال ثم دخل عليه رجل آخر فقال له مثل ما قال له الأول ورد عليه نحو ذلك قال فقال عثمان رضي الله عنه قالوا الزبير قال نعم قال أما والذي نفسي بيده إن كان لخيرهم ما علمت وأحبهم إلى رسول الله ﷺ
Its isnad is sahih. Bukhari reported it in 5/21 from Khalid bin Mukhlad from Ali bin Mushir, and Hakim reported it in 3/363 via Zakariya bin Adi, saying, "Sahih according to the criteria of the two sheikhs, though they did not include it." But it is in Bukhari as you can see, so his claim that it was omitted is a mistake.