The 36-storey building next to the Barbican – known as the Heron – has been the subject of a fierce bidding contest.
But senior Mace sources said the firm has lost out “by a mile” compared to McAlpine’s bid for the job.
The source told the Enquirer: “In truth we were nowhere near McAlpine’s bid and that has become a familiar story recently.
“They are pricing work at very low levels and most contractors can’t get near their prices.
“It’s getting to the point at the moment that if McAlpine are looking at a job you know you are going to really struggle to match their figures.”
Brookfield and Skanska were also interested in the scheme but the shortlist was whittled down to a two-horse race.
An official confirmation of McAlpine’s victory is expected shortly before construction work starts on the 248-apartment scheme for Heron and its chief executive Gerald Ronson.
Latest contract league tables compiled by Barbour ABI show that McAlpine jumped from tenth to fourth place among contractors in March after winning work worth £140m. Its average position for the year to March was 17th.