A spokesperson for administrator Deloitte & Touche said it had received several expressions of interest from companies hoping to buy all or part of the company.
Ballast Services employs 100 staff and is believed to be worth between £8m and £12m.
Five senior figures at the division, including managing director Phillip Cooper, have appointed an adviser to find a business partner and a venture capitalist to back a buyout.
A source close to the management said: "They are discussing opportunities to raise money – the team needs a business partner, somebody with a balance sheet."
Alfred McAlpine has also expressed an interest in Ballast Services. Ian Grice, McAlpine's chief executive, said: "Their FM and their PFI – we'll have a look just to see if there is anything there worth having."
Kier is understood to be thinking about buying the north-eastern construction division of the failed contractor.
However, Gleeson, which considered buying Ballast three months ago, has ruled itself out of a bidding war.
Several subcontractors across the country have lost money as a result of the difficulties at Ballast. One firm working on the East Lothian Schools PFI project, which Ballast runs as part of a consortium, is owed £500,000; another is believed to be owed £800,000.
ABB, one of the country's largest M&E contractors, is thought to be owed between £100,000 and £250,000.
The eight sites of the East Lothian Schools project are now at a near standstill as construction workers have been ordered off the site. Some electrical work is still being carried out by Forth Electrical Services, part of the Ballast consortium.
It is also uncertain whether Ballast will continue to work on a window replacement contract for Falkirk council.
A spokesperson for the council said: "There is the prospect that the contract will be one the administrators will see as saveable and a source of income. If the contract can be saved then this will save time retendering and will also be of benefit to local suppliers that are owed money by Ballast."