Ardmore is currently building the substructure for the 29-storey scheme under a separate £10m contract.
Construction information specialist Glenigan said the contractor is in a three-way race with Sisk and Brookfield for the main contract on City Road for developer Groveworld.
Ardmore also built the £18m first phase of the City Road Basin scheme which consists of a 15-storey residential tower.
One bidder said: “Nothing is certain in this current market, but you’d have to put your money on Ardmore considering they built the first phase and are on site with the substructure.”