The project will see the winning contractor install a huge ETFE roofing canopy similar to that used at the Eden Project, across the station concourse as well as carrying out other improvements.
Kier and Morgan Sindall submitted their final bids earlier this year and sources say Network Rail has called for more bid details from Sindall, which is rumoured to have submitted the cheaper bid.
Up to £16m of the cost will be Network Rail funded with the balance coming from Transport for Greater Manchester.
The improvements are intended to future-proof the station allowing for the imminent electrification of the line to Liverpool and would also take into account big improvements planned under the Northern Hub upgrade proposals.
Plans to improve Victoria station further include new shops and cafes, better Metrolink facilities, and refurbishment and renewal of the Grade II listed station building.
Construction is scheduled to begin next summer with completion by winter 2014.