Sandwell's NHS trust had aimed to have a contract settled with Balfour Beatty at the start of November but the agreement is still being held up.
Trust bosses wanted fresh work to begin on the Midland Met during December but with the contract still not tied up it now looks unlikely that will happen.
Toby Lewis, chief executive of the trust, has expressed his frustration with the hold-up on getting work going again, particularly after the Government gave the green light for the project to continue in October.
The £475m hospital is around two-thirds built at Grove Lane, Smethwick, and has been massively delayed by the collapse of construction giant Carillion.
Mr Lewis said the majority of details were agreed with Balfour but that "some detailed design reconciliation work" still needed to be finalised. He said he hoped that would be possible during the next fortnight.
Further red tape is also causing problems for the trust. Mr Lewis said a "discrepancy" between the agreed final business case and NHS financial improvement trajectories needed to be resolved urgently.
"It will not be possible to proceed nor sign a contract until that discrepancy is resolved," he said in a new report.
He continued: "As with any negotiation, nothing is agreed until everything is agreed, by at the time of writing there are no obvious reasons why we will not be able to achieve contract signature in the next two weeks.
"I do recognise that we had targeted an October 31 and then November 30 deadline for same. We would hope that the extra time taken has assisted Balfour and others to ensure that start on site proceeds at pace."
Mr Lewis told the Express & Star last month it was unlikely work would start before the year if the contract was not agreed before the start of December.