The first trust to be affected is North Bristol, which is currently in discussions with the DoH about how much compensation it might pay to the runner-up in its tendering process for a new£374m PFI hospital.
The issue arises out of the new 'competitive dialogue' procurement process, adopted by the DoH in January 2006.
This process is designed to allow bidders and contractors to discuss all aspects of the contract during the bidding process. Under the new procedures, final tenders will contain all the elements necessary for the project to go ahead.
This is in contrast to the old competitive bidding process, which the EU felt was wrong for most large-scale public sector projects. But the changes mean the procurement process is longer and more detailed, creating extra costs for bidders who reach the final stages.
The EU public procurement directive does not say compensation must be given to unsuccessful bidders, but states that 'contracting authorities may specify prices or payments to participants in the dialogue'.
However, the DoH has now decided to explore the idea.
A spokesperson said that only the second-place bidder would be compensated and just from the stage when the bidding was down to the last two.
She added: 'It must be remembered that bid costs are all ultimately recovered from the public sector in terms of overheads on future bids. It is therefore in our interest to manage these costs in the most cost-effective way.'
North Bristol trust director of projects David Powell confirmed that discussions were under way with the DoH.
The trust launched its tender document for a new£374m hospital on 16 May.
Mr Powell said the trust was 'seriously considering' compensating losing PFI bidders for some costs, although 'nothing has been decided yet'.
He added: 'Although this has not been done in the health sector, we are considering recompensing losing bidders for some of the increase in their costs that will result from the increasingly detailed design work they will need to do as a result of the new competitive dialogue process. This detail will enable us to proceed with our scheme more quickly.'