The rail upgrade scheme, known locally as NUCKLE, will see two new stations and improvements at two others to raise capacity on the line.
A separate contract will be let for the delivery of the rail signalling systems, requiring the successful station builder to liaise with the firm selected to deliver the rail line improvements.
Works estimated to be worth up to £10m will include a new bay platform at Coventry station, new two-platform stations at Coventry Arena and Bermuda Park, as well as extension of the existing Bedworth station platforms.
Train frequencies between Coventry and Nuneaton will also be increased so that there is a train every 30 minutes.
PQQs are available to from 7 January on the council website.