Developers have submitted plans to Westminster council to convert parts of the West End landmark that would also include a community centre.
The Aziz Foundation, an education charity for British Muslims, has proposed transforming the former basement cinema that has been derelict since 2006 and parts of the ground floor in Rupert Street for use for praying and events.
The foundation is owned by Asif Aziz, who set up property giant Criterion Capital and in 2005 bought the London Trocadero and Piccadilly Hotel for £225 million.
A spokesman said surveys had revealed a “significant shortfall in the amount of prayer space for Muslims living and working in the West End” with only three in the area.
The application has received more than 250 comments on the council website.
Some have objected to potential increased traffic, with others claiming that a place of worship is not in keeping with an area famous for its bars, clubs, casinos and nightlife.
The proposed mosque site received permission for use as a community and arts centre in 2018. Planners are expected to decide later in the year.