A spokesperson for the contractor said: "Negotiations have gone past the point of major confrontation and are in the process of being finalised."
The negotiations between the two parties are based on an assessment of the specification problems carried out by Babtie, a consulting engineer that certifies specifications – although it is understood that Laing and the DTI disagree over how to interpret its data.
A source close to the DTI confirmed that talks were going on, but added that the department was refusing to water down its demands. "There are solutions being proposed, although whether they are acceptable is not clear. The DTI is steadfast that the building will adhere to the specifications in the contract."
A project team insider said that after reading Babtie's assessment, the DTI was not sure whether it was getting what it had asked for. But he confirmed that Laing and the DTI were continuing to negotiate on how the laboratory's stringent specifications should be interpreted.
He said: "Once agreement is finalised on particular points of the specification, Babtie has to begin re-certifying, which is complicating the whole process."
The Babtie study, which has already taken more than a year, was paid for by Laing and the DTI.
The project ran into serious problems over the high-specification air-conditioning systems that were required in some of the development's laboratories.
Negotiations have gone past the point of major confrontation and are being finalised
Some facilities were handed over to scientists then taken back and reconstructed after they failed to meet set tolerances.
Laing called in American troubleshooter Bechtel in July to help complete the project.
The company is pursuing M&E contractor NG Bailey for some of the £40m it has lost so far.
The two firms are understood to be seeking an out-of-court settlement in which Bailey compensates Laing for some of its losses.
It is understood that Bailey has paid £3m so far, and does not expect to make a profit from the project.
The National Physical Laboratory was one of several live projects not taken over by concrete specialist O'Rourke when it bought Laing Construction.