The Enquirer understands that developer the Beetham Organisation is racing to beat a deadline later this month to take the site back from administrators at BDO.
Mace is believed to be in the box-seat to win the job if Beetham is successful.
The project to build a 52-storey tower was put into administration by bankers RBS last October when Beetham fell out with its Russian development partners
But Beetham wants to get the job going again and is hoping to beat off rivals for the scheme and seal a deal by the end of this month.
A spokeswoman for administrator BDO told the Enquirer: “Negotiations with interested parties are ongoing”.
She declined to name bidders or confirm any timescale for a deal.
The site has planing consent for a 52-storey skyscraper containing 64 luxury apartments and a 261-bedroom hotel.
One contractor said: “This will be great news for the industry if this scheme gets going again and the word is that Beetham will go with Mace if they gain control of the project again.”