The third bid led by Costain with Sir Robert McAlpine is believed to have dropped by the wayside.
O’Rourke is working with Bouygues and Balfour with Vinci on their bids.
The fact that Costain and Sir Robert McAlpine had no French firm in their bid team is believed to have counted against them with French client EDF Energy.
A source close to the project told the Enquirer: “It has officially been a three-way race but in reality it has been a head-to-head contest for a couple of months now.
“Big hitters from O’Rourke and Balfour have been the only people in talks with EDF for a while.”
Industrial relations will play a key role in who will win the Hinkley job.
The source said: “O’Rourke has the directly employed workforce to cope with a job needing 1,500 workers.
“Balfour has been at the forefront of disputes in the M&E sector but its sudden change of heart in that may have been influenced by its need to have stable industrial relations for bids like this.”
An EDF sokesman said: “We do not comment on contract awards while the process is live.”