Mustadrak al-Hakim — Hadith 7260

It is narrated from Abdullah bin Salimah that he said: I and two other men, one of them from among us and one from Banu Asad, I think, came into the presence of Sayyiduna Ali bin Abi Talib (may Allah be pleased with him). He sent the two of them on some mission and said: You are both strong men, so strive hard in the matter of your religion. Then he went to relieve himself, and when he came out he took a little water in his cupped hand and wiped (his hands and face) with it, and then began reciting the Qur'an. He sensed that we were surprised at this, so Sayyiduna Ali (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings be upon him) would go to the toilet and relieve himself, then come out and eat bread and meat with us and recite the Qur'an, and nothing kept him (peace and blessings be upon him) from reciting the Qur'an except janabah (major ritual impurity).
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.