A winning bidder will be named in December to allow a start on the project early next year.
The major flyover project forms part of the reading station redevelopment and will allow mainline passenger services to travel over the top of freight trains up to a mile long coming up from the south.
The project is one of two big viaduct jobs presently being tendered in the south east.
Network Rail is also assessing bids from Carillion, Morgan Sindall and Skanska for a £50m contract construct a larger flyover at Stockley in Hillingdon. This will enable Crossrail services to operate to Heathrow.
The Hillingdon contract is expected to be awarded in November.