The team, called BCJ, which also includes Balfour Beatty, the Maeda Corporation, Kumagai Gum and China State Construction, is in talks with client Hong Kong Airport Authority.
A source close to the negotiations said that a mediation meeting is due to be held next month to try to reach a compromise.
The source added that if this was not successful the parties would go to full-scale arbitration, which would take place in late summer.
He said unless the consortium changed its claim dramatically, arbitration was the most probable outcome. However, an Amec statement this week said it was looking to resolve the issue in the near future.
The statement confirmed that the two parties were in talks. It said: "The joint venture team is currently in negotiations with the client over contract settlement for the airport contract, but the details are confidential. There are no new claims on the table between us and the client."
The statement said the contractor hoped the dispute could be speedily resolved. "We do not want to enter into a protracted legal wrangle with the client; our objective is to seek fair payment within a reasonable timescale. We are looking for fair treatment and we do anticipate making progress in the near future."
It is understood that claims worth £80m have already been resolved.
An airport statement said it was unable to comment on the claims. It said: "We are not in a position to disclose any details related to claims as it is commercially sensitive."
Amec's dispute is part of a torrent of claims that has hit the airport since its completion three years ago.
According to the Hong Kong government, outstanding disputes worth a total of £567m still hang over the airport.
Most of these relate to the late handing over of the scheme, which was to have been completed in 1997.
Problems experienced during the project included a change in the use of terminal areas and difficulties with the roof and structural steel. Defects also emerged in some of the glass used.
The source close to the Amec dispute suggested that the fact that Hong Kong Airport Authority lost £15m in the year to 31 March 2000 might be influencing its conduct.
He said: "It is an unbelievably hard process. [The airport authorities are] using all the instruments they can to slow down the process until the revenue comes in."
Another source claimed that there were political sensitivities surrounding the scheme that had to be take into account. He said: "Being a public authority, there is a lot of concern about it paying contractors a lot of money. It's very sensitive."
The source said the whole airport project, one of the biggest civil engineering projects in history, had been affected by the claims.
It is understood that there were about 6500 lodged for the entire £12bn scheme. Of these, about 4500 are believed to have been resolved.
The source said: "The project is an absolute disaster. It was the biggest project in the world but also the biggest disaster."
Chek Lap Kok: Subject to delays1992 Chek Lap Kok airport scheme given the go-ahead
1994 The £1bn terminal building at the airport is approved
1995 Contractor BCJ signs the contract for the airport deal
1998 The terminal, the world’s largest single airport building, is handed over to client Hong Kong Airport Authority a year after it was originally planned to open.