The Enquirer understands that Costain is edging ahead of rival bidder Balfour Beatty for the planned major upgrade between junctions 21a and 26.
Highways England is hoping to start work before the end of this year on the latest 11 mile stretch of motorway to be upgraded to All-Lane Running.
One industry source said: “There’s been quite a battle going on for this job but it looks like Costain are emerging as favourites now to land it.”
Costain declined to comment.