The next stage of development would provide an extra 44,000 sq ft (4,085 sq m) of retail space in two medium-sized units as well as 124 apartments.
The application follows the completion last year of phase two of the centre’s extension.
The work on the Surrey scheme would begin by the end of the year if the council gives its approval. It covers 250,000 sq ft (23,225 sq m) at present and is anchored by Marks & Spencer, Bhs and Woolworths.
Trevor Colman, managing director of Colman Architects, which represents Clerical Medical Investment Group, said: “The third-phase works will provide Staines with a modern and dynamic extension to the centre.