Balfour Beatty, Carillion and Capita are also believed to be in the hunt for Mouchel who confirmed the refinancing deal to the City this morning.
Mouchel is looking to sell-off non core businesses to raise cash for a £30m staged payment due in March 2012 which is part of the refinancing agrement.
If the consultant misses the payment, interest rates on the rest of the funding package will shoot-up.
Chief executive Richard Cuthbert said: “This is an important turning point for Mouchel. It provides the Group with stability and ensures that we can continue to compete successfully in our chosen markets.”
Advisers have been appointed for the non-core sales and Mouchel is hoping to claw back £20m in disputed payments across its Middle East operations.
Costain has already made three public bids for the whole of Mouchel valuing the consultant at £175m.
The City expects a bidding war to continue among potential suitors but Balfour and Carillion might look to snap-up operating divisions rather than the whole firm.
The statement added: “Costain’s interest has been made public, and shareholders will be aware that we rejected its early approaches because they significantly undervalued the Company and its prospects.
“We are actively reviewing all of the approaches that we have received and our other options. Our priority remains enhancing shareholder value and we continue to urge shareholders to take no action.”