The bidders, who gave their best and final offer in the summer, said it was going through the Ministry of Defence's approval process. All large defence PFI schemes now have to go through the MoD's Investments Approval Board. Previously, the board assessed only equipment purchases.
One bidder said the approval process could see the scheme pared down. He said: "If the project doesn't hit the public sector comparator, the price may have to be negotiated back."
A consortium led by Carillion and another team including Mowlem, Atkins and defence contractor Hunting are competing for the project, launched in 1999.
The two consortiums were shortlisted for the project last year.
The scheme involves running the school's 881 ha estate in Kent and Surrey, and providing skills training to army engineers.
The contract will be for 10 years and could be extended to 25 if a capital works programme is started.
One bidder said a lack of urgency was to blame for the delay in the scheme's programme. The bidder said: "This is not like Allenby and Connaught [two large barracks schemes], where they have to house soldiers by a certain date. There's not as much pressure on this one."