The work on Lower Thames Street near Cannon Street railway station is worth around £100 million.
Skanska, Sir Robert McAlpine and HBG are all working up bids for the job which will go back to client Pace Investments at the end of the month. A fourth bidder, Bovis Lend Lease, is also believed to be pricing the deal.
McAlpine is already on site at the neighbouring £150 million Waterbank Place scheme - formerly known as Mondial House - which it is building for a joint venture client of UBS Global Asset Management and London developer City Offices.
Bidders expect Pace to decide a winner fairly quickly.
Clients are scrambling to get work started before construction on the 2012 Games venues begins in earnest next year.
One bidder said: "They want to crack on with this before resources go elsewhere and they're looking at a start in the early part of next year."
Both McAlpine and Bovis have lined up work on the London Olympics site but the bidder said: "We've looked at the Olympics but most of the big jobs are starting to go. We're still interested in [the Games] because there's a lot of work but there's a lot of [office] work out there like this job which means we're pretty full up at the moment."
Helical Bar is development manager on the 11-storey block with David Walker Architects the designer.
Key City of London office projects
Bovis Lend Lease 201 Bishopsgate and Broadgate Tower (£201m)
Bovis Lend Lease Leadenhall Building (£281m)
Sir Robert McAlpine Watermark Place (£150m)
Skanska The Walbrook (£150m)
Skanska St Botolphs (£110m)
Sir Robert McAlpine Drapers Gardens (£80m)
Multiplex Pinnacle (£500m)
Bovis Lend Lease Aldermanbury Square (£72m)
Skanska Heron Tower (£500m)
Sir Robert McAlpine New Street Square (£200m)
Mace 51 Lime Street (£117m)
Mace 20 Fenchurch Street (£205 m)
Bovis Lend Lease 1 New Change (£205m)