The hotel and student flats project is understood to have attracted bids from Bam, Shepherd, Vinci, Sir Robert McAlpine, Ocon and Watkins Jones.
The 180,000 sq ft Spring Mews scheme is expected to cost around £50m to build and will include 408-bed student accommodation and a 120-bed budget hotel.
Around these CLS aims to build 30,000 sq ft of shopping units and 50,000 sq ft of offices as well as a replacement community centre.
Work is expected to start on the project in the late summer.
The scheme is on a separate site half a mile from the proposed Vauxhall Square development.
This £250m sq ft mixed-use development will include two towers and an aerial walkway.
Sten Mortstedt, Executive Chairman of CLS, said: ”These mixed-use proposals can provide substantial investment and regeneration into the Vauxhall area while meeting the significant demand for student accommodation and hotel rooms in central London.
“As a long-standing local Vauxhall based company, we are pleased to be able to work together with the Vauxhall Garden Community Centre to provide a brand new community centre facility within these plans.”