Contractors Laing O'Rourke, Mace and Sir Robert McAlpine, are understood to be in the running to construct Europe's tallest building, the £350m London Bridge Tower project.
Multiplex managing director Martin Tidd insisted that it also had a bid on the table with developer Sellar Property Group, despite reports that the firm had pulled out of negotiations.
Skanska and Bovis Lend Lease appear to have ruled themselves out. Skanska is about to build the £600m Heron Tower in the City, and is rumoured to have an agreement with Gerald Ronson's Heron Group to work only on his skyscraper until it is completed.
Sellar Properties is understood to have invited contractors to pitch this month and will select a winner by the end of August.