Carillion is in line for the contract for the tallest building ever built in the UK outside of London.
The firm is the preferred construction partner of developer Beetham for the £150 million residential tower on the corner of Deansgate and Great Bridgewater Street in Manchester city centre.
Carillion's package is valued at around £60 million.
The tower will feature 219 one- and two bedroom luxury apartments over 47 storeys at up to 157 m in height.
A glass blade on top of the tower will reach up to 171 m. It will be the tallest residential tower in the country, dwarfing the previous record holder, London's 128 m Barbican tower.
It will also house a 23,000 sq m five star Hilton hotel and 7,000 sq m of office space.
Beetham has just released the first artist's impressions of the tower, designed by Ian Simpson Architects, following its application for planning permission to the city council in June. A decision on whether to give the scheme the go-ahead is expected in October.
Work on the job is expected to start on site in March next year.
Carillion is also working with Beetham on a smaller 30-storey, £60 million tower in Liverpool.