Laing's construction arm completed an extension to The Lanes shopping centre in Carlisle city centre last year.
Negotiations over the final settlement were delayed by its acquisition by O'Rourke. O'Rourke may now claim about £2.5m in disruption damages after rejecting an agreement made in principle between CGNU and Laing.
A project insider said O'Rourke's management was not happy with a deal put forward by Laing for the cost of additional works to conclude the project.
The insider added that O'Rourke is expected to lodge an initial claim of £2.5m against CGNU, but it could increase this after completing its examination of the project.
He said: "O'Rourke feels a court would award it more money. This is why it is not accepting the Laing agreement and is putting in a new claim."
CGNU refused to comment.
O’Rourke feels a court would award it more money
An O'Rourke spokesperson would not be drawn on the details of the claim. He said: "Laing [Construction] has been negotiating the final account over the past year, and negotiations are close to a conclusion."
A Laing insider said the project had been handed over normally and Laing was now settling the final account. He confirmed that the project did have problems and additional works.
He said the project's problems had been caused by complex demolition work involved in the scheme. He added there was also a planning issue, which had caused time delays.
O'Rourke completed the acquisition of Laing for £1 in September. The finalising of the deal was delayed as O'Rourke picked through 63 contracts during a six-month due diligence period. O'Rourke acquired 50 of these contracts.
The £16m Lanes shopping centre extension was completed last year. The development, which was partly backed by Carlisle council, was extended to the north to provide 25 units with stores such as Gap, H&M and Dixons. The scheme is anchored by a 9300 m2 Debenhams store.