The contractor said: "It has come out of the blue. We are not sure we have the upfront design people to deal with it."
Another said he expected that only two or three firms would tender. Bid costs are expected to be at least £10m, with £2m needed for the design alone.
The contractor said: "It looks like you will be getting a situation similar to the Bart's job [a £1bn hospital PFI in central London], where only Skanska and Bouygues put in bids."
Major Contractors Group director Bill Tallis said market capacity was an issue for PFI hospitals. Potential bidders seemed to have difficulty finding the working capital and the design skills required.
Tallis said: "Markets do not cope well with peak-hour flows. In the rush hour you don't get a seat on the Tube."
Nigel Hodson, the NHS director of the project, said he was aware of the situation in the industry. He said: "We couldn't go to the market now. That is why we are waiting for the full tender to be sent out later on in the year."
Hodson said the client had held an open day for contractors last month and was hoping to hold one-on-one discussions in the next two months.
A source close to the NHS hinted that bidders for the scheme could come from Europe and the USA.
He said that if a firm could not be found for the entire scheme, it could be split into "three to four bite-sized pieces".