HBG is set to sign a £25 million arts deal in Devon.
Sources at rival firms said Plymouth University would appoint HBG preferred contractor to build an arts centre in the city centre by the end of the month.
Cowlin, Laing O'Rourke and Sir Robert McAlpine were all shortlisted. Several bidders believe a fourth contender, Costain, came the closest to beating HBG.
As well as providing new facilities for the university, the block will rehouse Plymouth Arts Centre, which will move from its current premises in Looe Street.
One source said: 'It became a two-horse race between HBG and Costain. HBG already has some work in the area so they were always the favourites.'