The firm, which is building the £840m Glasgow Southern General Hospital, was told this week it had failed to make the cut for the next stage of the £450m Royal Liverpool Hospital.
Teams featuring Balfour Beatty, Carillion and Spanish contractor FCC are all through to the next round of bidding, which is being masterminded by Royal Liverpool & Broadgreen University Hospitals NHS Trust.
Two bidders will be chosen by the end of the year with a preferred due next June ahead of financial close being wrapped up by the end of next year.
But the scheme is set to face a legal challenge from a campaign group opposed to PFI.
Keep Our NHS Public is hoping to win a judicial review to look into the business case of the new hospital and whether PFI offers better value-for-money than a traditional procurement route.
The Department of Health has responded to the group’s claim, launched at the end of June, but declined to comment further.
Lawyers for the group say they will be writing to it shortly to advise on whether to press ahead with an application for permission in the High Court for judicial review.