Officials at client Havering Hospitals Trust were locked in talks this week over what to do about the overruns of up to £10m, which have been caused by design changes to M&E services.
The project also faces delays because the trust has so far failed to buy land for the site in the centre of Romford from Havering council.
The deadline for buying the land was due to lapse at midnight on Thursday 31 October.
Speaking on Wednesday, Peter Murphy, the trust's chief executive, said: "We will be putting out a statement later in the week, there is a meeting today to discuss the future of the scheme – but decisions taken will, for the time being, remain confidential."
An insider at Havering council said its members were considering five options.
The first was to hold the consortium, Catalyst, to its original bid – which would force Bovis Lend Lease to incur additional cost or pull out.
A second option was to try to secure more funding to meet the deficit.
A third was to install the improved M&E design and pay for it by decreasing the cost of the rest of the hospital.
The fourth option was to redesign the hospital, and the final one was to give the job to the losing consortium, which contains French contractor Bouygues.
There is a meeting today to discuss the scheme’s future
Peter Murphy, hospital trust chief
The source added that Havering council, which first agreed to sell the land two years ago, was now reconsidering its decision because of the delays in finalising the sale caused by the design changes.
The insider said: "The deal to buy the land for more than £20m was arranged two years ago; a deadline for that deal was set for 31 October 2002 but it still hasn't been agreed."
He said the council now took the view that the land was now worth more than £20m.
A spokesperson for Catalyst confirmed that there had been capital cost increases on the project. He said that, in addition to the upgraded M&E specifications, there would be minor changes to the facility's construction grids.
He emphasised that the changes would not affect the hospital's clinical facilities and would give the hospital extra space. He said he was aware of the problem over the land but said that was a matter for the trust to resolve.
The project team includes QS Cyril Sweett and architect Building Design Partnership.
Havering Hospitals Trust was chosen last year by the government as one of three pilots to test the practicalities of keeping staff on NHS terms and conditions when they are transferred to the private sector in PFI hospitals.
The other hospitals were Stoke Mandeville Hospital, Buckinghamshire, and Queen Mary's Hospital in Roehampton, south-west London.
Under the pilots, all cleaning, laundry, catering and security staff will remain NHS employees and keep their conditions with pay protected.