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I am pretty sure this mosque is Masjid Hannana. There is a story that as Hasan and Husayn were carrying the body of 'Ali from Kufa to Najaf, they passed near this mosque. As they were passing, the pillars of the mosque inclined towards 'Ali as if bowing down and paying it's last respects. Also, it is said that a piece of Husayn's face is buried here. This mosque is directly between the Great Mosque of Kufa and 'Ali's tomb, and so 'Ali's body probably would have passed through here, making this mosque a good canidate.(http://www.al-islam.org/ziyarat/iraq.htm)