Allen has confirmed that two contractors have bid for the contracting arm, along with the group's former chief executive Ken Fox and chairman Ron Greenhalgh.
But mystery surrounds the identity of the third bidder after contractors operating in the north of England, such as Morgan Sindall, Gleeson and Shepherd, confirmed that they had not entered the ring.
Kier, another group touted as a likely bidder, is understood to have pulled out.
Analysts believe that Fox and Greenhalgh, who left Allen to launch their bid, are favourites but one contractor who considered making a bid said the process seemed fair.
"We were concerned that it would be uncompetitive because of the MBO bid but we were assured that the process would be kept honest and competitive." YJL, which has a turnover of £202m, has bought three construction businesses in the past year, including contractor Britannia for £13.3m.
Earlier this month, YJL lifted its stake in buildings materials group Cape to 16.84%, leading to speculation that it might be considering a bid.
The sale of Allen's contracting arm is part of a restructuring plan that will see the group focus on equipment hire and rename itself Speedy Hire.