Construction information specialist Glenigan reported that Skanska, Mace, Lend Lease and Sir Robert McAlpine were in the hunt after the scheme was granted planning permission in January.
But sources close to the project said it is now a two-horse race between Skanska and Mace.
The source told the Enquirer: “Four were in the main running originally but Skanska and Mace have emerged from the pack and it looks to be between those two now.”
US insurance giant W R Berkley is the client behind the 38-storey tower next to the Lloyds Building in the heart of the City of London.
Its planned 190m tall European headquarters building has been designed by Kohn Pedersen Fox, also the architect behind the Heron Tower which was built by Skanska.
The insurer will directly fund the £500m building at 52-54 Lime Street, which is expected to break ground this year for completion in 2017.
A winning contractor is due to be appointed before the summer.
KPF’s design resembles an upright scalpel with floor plates varying from 9,000 sq ft to 22,000 sq ft arranged around a side core that optimises floor dimensions and limits solar gain.
The project will also create a 11,000 sq ft public ‘square’ to boost the existing precinct around the Willis Building.
William Berkley, founder and chairman of W R Berkley, said: “With the continuing expansion of our operations here, it makes sense to invest in a landmark building which will provide a strong base for that growth.
“This major investment is a signal of our belief and confidence in London as the centre of the global insurance market.”