Developer Citygrove told the Gazette this morning (Tuesday) that it had sent its application to Hillingdon Council and expects it to be considered this year, with a possible start to work in early 2014.
The £85m scheme will include an 11-screen Cineworld cinema, Nando’s, Frankie and Benny's and Chiquitos restuaurants.
The plans for the 11-acre site include 104 family homes, an Asda supermarket plus public plaza, seating and play area.
The site, off Victoria Road, used to be a dairy but closed in 2006 and has been derelict since.
A small part could house an access shaft for the HS2 tunnel which would pass to the south-west of the site. Construction is expected to be complete by June 2015, two years before HS2 building would begin.