The move would mean a Laing O’Rourke and Mace joint venture has missed out along with bids from Balfour Beatty and Carillion on the latest round of the Thameslink investment programme.
Plans include a new concourse that is bigger than the pitch at Wembley, which will sit underneath the tracks.
Two new entrances will be constructed on Tooley Street and St Thomas Street, which will improve links between the areas around the station.
Network Rail said it hopes to have chosen a main contractor on board by the end of the year.