Laing and Bailey are understood to be seeking an out-of-court settlement that would see the specialist contractor compensate Laing for some of its losses.
The project has run into serious problems over high-specification air-conditioning systems needed in some of the development's laboratories.
But if this deal fails, the battle over who is liable could end up in court. Rumours were circulating among site workers last week that Laing is already preparing to sue Bailey.
A senior project insider said talk of court action was premature and "overstated". He said the companies were looking to come to a financial arrangement.
Laing refused to comment and Bailey said it was not in a position to comment. Bailey said last week that the requirements of the job were not achievable.
The laboratory is the only live Laing contract that will not be taken over by concrete specialist O'Rourke. That deal, which saw Laing pay O'Rourke £30m to take the business off its hands, is due to be finalised this month.
How can so much money be lost in one project, and how could Laing let it happen? This is crazy
NPL site construction worker
US troubleshooter Bechtel, which Laing brought in to help it complete the project, has been on site for two weeks and met joint client the DTI on Monday. Bechtel is to give to the Laing/Serco joint venture cost analysis advice on how best to deal with the problem.
It has emerged that the advanced technology division of architect BDP has also been brought in to oversee aspects of the design. BDP declined to comment, citing "potential litigation".
The technical problems with NPL's air-conditioning are expected to delay the project for a year. It is now due to be completed next spring.
Construction workers interviewed when Building visited the NPL site last week were unsure how the losses had been allowed to mount so high before Bechtel was brought in.
One said: "How can so much money be lost in one project, and how could Laing let it happen? This is crazy." Another added: "I've been here for 18 months and it has been a mess from the start."
Workers said Laing and Bailey were locked in a dispute over who was to blame. "The lawyers are involved now, so where this ends is anyone's guess," one commented.