Tomorrow, Strathclyde Partnership for Transport is expected to agree the contract should be awarded to Graham Construction which has a base in the city.
The upgrade is part of the transport body's plan to carry out improvements to all 15 Subway stations in advance of driverless trains being introduced.
Hillhead, Partick and Ibrox stations are complete and work at Kelvinhall will be finished in time for the Commonwealth Games.
SPT say the works at St Enoch will take the same high quality approach as the previous stations creating an environment which is clean, efficient, more modern and passenger friendly.
It involves replacing materials on the floors, walls and ceilings throughout the station and improving passenger signs.
Lifts will be introduced for the first time on the Subway allowing disabled passenger to travel to Govan station which will also have lifts.
That will allow travel from the city centre to a key interchange with Fastlink and the bus station and will allow onward travel to the new South Glasgow Hospital.
Work will take 15 months with only non-intrusive construction happening before the Commonwealth Games.
Two new glass and steel station canopies will create a flagship city centre station for the Subway.