Two bids led by Laing O’Rourke and Balfour Beatty are left in the race for the job which will employ 1,500 workers.
O’Rourke is working with Bouygues and Balfour with Vinci.
Both teams are still confident of victory for what will be the industry’s biggest single contract win for years.
A source close to the project told the Enquirer: “This one is really going down to the wire and both bidders have thrown everything at the tender race.
“It will be a huge win for the successful bidder and provide a guaranteed work stream on the site for years.”
An EDF sokesman said: “We do not comment on contract awards while the process is live.”