It has been soundly established that Abū Hurayrah performed wuḍūʾ on the roof of the mosque; the report is recorded by Aḥmad and Muslim.
This ḥadith indicates that performing wuḍūʾ inside a mosque is permissible. Al-Nawawī states in his commentary on Muslim: “Ibn al-Mundhir has transmitted the consensus of the scholars that it is allowed, so long as it does not cause harm to anyone.”
I add: Al-ʿIrāqī, in his commentary on the Taqrīb, writes: “Ibn Baṭṭāl related its permissibility from the majority of scholars, while he transmitted from Mālik and Sahnūn that they deem it disliked, out of deference to the mosque.”
I say: the ḥadith itself stands as evidence against their view.
That said, nothing contrary to the Sharīʿah should accompany the act, as happens today in many mosques supplied with Fijeh water. The forceful rush of water from the taps and its impact on the tiles create a loud noise that disturbs those praying. For this reason we deem it essential that the ablution area be placed in a confined space adjacent to the mosque, not inside it, as is the case in the ʿĪsā Pasha Mosque opposite the Ḥamīdiyya market and elsewhere.
10 – Gathering and forming study circles for recitation of the Qur’an and for learning. The proof is the ḥadith:
“While he was sitting in the mosque with the people around him, three men arrived. Two of them came to the Messenger of Allah ﷺ while one went away. When the first two reached the Messenger of Allah ﷺ they greeted him. One of them noticed a gap in the circle and sat in it, while the other sat …”