The application has been submitted by Mohammed Naeem, chairman of the Mosque’s board.
The flats,if approved, would be built near the old entrance of the ongoing development in Cumbrae Terrace.
He is seeking planning permission in principle to build on vacant land within the Mosque’s boundaries to house the Masjid’s two Imams in addition to renting the other two as an additional income for the place of worship.
Mr Naeem said: “We currently have permission for two flats but we want to build another two as we don’t know how many Imams we will have at any one time.
"The flats will be built where the old entrance was at Cumbrae Terrace which is now blocked off.”
He added: “As a registered charity any income made from renting the proposed properties will go towards the completion of the Mosque.”
Councillors and officers will consider the application in due course.