It is understood that McAlpine and Mace will form a joint venture to pitch for the £200m package, which is being managed by developer and project manager CIT.
The work, for three of the remaining six plots on the Southwark riverside site, is to be procured under a traditional JCT contract.
This is a change of procurement method for CIT, which is running the GLA headquarters project under a construction management deal with Mace.
A source close to Sir Robert McAlpine and Mace said they were looking at sharing the work, which is tipped to include the headquarters of GLA arm Transport for London.
The source said: "McAlpine will underwrite the scheme while Mace will supply the bodies." CIT commercial director George Kyriacou refused to comment on the developer's choice of contractor.
He said: "We are in advanced discussions for at least one of those three plots. We will probably be deciding in the next couple of weeks." Kyriacou said the developer was not necessarily looking at a sole contractor for the work. He said: "We are looking at different combinations." The three buildings have all been designed by Foster and Partners, architect of the GLA headquarters.
When complete, the More scheme will consist of up to 10 buildings, with office, retail and leisure facilities including a hotel, cafes, bars and restaurants.
Detailed planning permission already exists for the complete development, which will total 235,000 m2. The masterplan for the development was also completed by Foster and Partners.
Work on the infrastructure, which includes pedestrian areas, landscaping and underground servicing, has already started.
The GLA headquarters, on the north-east corner of the site, is set to be completed in April 2002.
Mace won the GLA building contract in 1999, beating off rivals Exterior and Schal.
