The construction cost of the scheme, which has been masterplanned by Building Design Partnership, is expected to be £400m.
A source at one of the bidders said the firm that won the contract could find it was then asked to become the main contractor. Site work is expected to start next year.
The project, in partnership with Liverpool council, is on a 17 ha site called the Paradise Street development area. It will include 148,000 m2 of retail space, 21,500 m2 of leisure space and 364 houses and flats.