Two contractors emerge as frontrunners for 80,000-seat venue, expected to be tendered later this year.
Building understands that both have received union advice on likely terms for the key stadium contract, and are considering bids for the project.
The Olympic Delivery Authority is expected to tender for the position before the start of next year.
Laing O'Rourke has been widely expected to pursue the contract after acting as an official sponsor for London's Olympic bid. Bovis, which built the Olympic village for the 2000 Games in Sydney, has not previously been linked with the job.
A source close to the Olympic bidding process said: "It makes sense for these companies to go for the contract. I know there is a lot of excitement surrounding the role."
A Bovis spokesperson said: "The stadium is certainly a project we would consider. We have a good track record on Olympic work in Atlanta and in Sydney."
The contract to build the 80,000-seat stadium in the Olympic park is expected to be tendered later this year, alongside tenders for the stadium design.
The Olympic organisers are known to be keen to appoint contractors early on in the design phase to encourage the integration of the project teams working on Olympic contracts.
David Higgins, the Olympic Delivery Authority's chief executive, announced earlier this month that stadium construction would begin in 2008. In a timetable for Olympic projects released at a business summit in Canary Wharf, he said he expected tenders for the stadium design to be sent out in July.
Building understands the London 2012 bid team used a budgeted figure of £280m for the stadium in its presentations to the International Olympic Committee in Singapore in July.