Sources close to the project claim a deal has been struck to incentivise the construction consortium carrying out the work to complete it by the end of this year.
Project chiefs last week admitted to MSPs there was still a “large amount of work to be done” but said they were confident of hitting their target.
They also said the overall cost of the bridge would be between £1.32 and £1.35 billion against a 2009 estimated cost of £2.34bn.
It is understood the incentive to finish by December is outwith the fixed-price contract to build the Queensferry Crossing.
It is also believed the construction firms involved will lose hundreds of millions of pounds as they have had to absorb all of the scheme’s extra costs.
Construction of the viaducts and piers of the bridge are behind their original schedule, with work on the deck of the crossing not scheduled to be finished until September, with up to 19 weeks of fitting out then still to take place.
And in January we revealed details of a “grace period” for constructors where as long as the bridge opens between December and August next year the consortium will not be liable for financial penalties typical in delayed construction projects.
Addressing MSPs last week, project director David Climie was asked if he was still confident of meeting December’s deadline.
He said his team was “focused absolutely on achieving the original target date for opening to traffic and to a significantly reduced budget”.
But he admitted that poor weather meant they had “not made as much progress as we would have liked,” before adding the target date was “still do-able”.
Scottish Labour deputy leader Alex Rowley said: “We need full transparency from John Swinney about whether or not bonuses have been offered for this project.”
A Forth Crossing Bridge Constructors spokesman said: “The points raised are commercially confidential.”
A spokesman for Transport Scotland, which is overseeing the project, said details of its contract with engineers were confidential, but he added that “by its very nature” it was incentive-based.