The council advertised the work in the Official Journal last May, with tenders going out two months later.
Bluestone estimates the value of its work would be worth £30 million over five years. The other three contractors have yet to confirm exact numbers with the authority and a meeting is scheduled to take place later this month to thrash out exact workloads.
One source said: 'We are on the framework but we can't discuss the value until we've met with the council again.'
Another firm admitted: 'I don't think we've even signed it yet. We don't know exactly what it will involve nor how much we'll get but it's great just to get on it.'
The framework deal will cover the council's £25 million-a-year schools modernisation project, which includes tackling an £85 million maintenance backlog. Work includes new build, refurbishment, repair and maintenance, asbestos removal, demolition, site preparation and clearance work.
Landscaping and specialist- trade construction will also be included. Construction work will start in early 2006.
The contract comes after the council failed to get funding for the first wave of the Government's
Building Schools for the Future programme and was put to the back of the queue for waves 13-15. Last year the council was blasted for advertising its BSF programme prematurely.