The proposed relief road would bypass heavily-congested areas in Bramhall, Cheadle Hulme, Hazel Grove and Handforth.
Stockport Council aims to get a contractor on board by August to work up design details for construction work to start in October 2014 in the hope of completing the £140m road job in May 2017.
The scope of the work includes completion of the detailed design, construction and defects liability maintenance of dual carriageway running from the A6 at Hazel Grove to the Ringway Road / Ringway Road West junction, incorporating an existing section of the A555.
It incorporates seven new and five improved junctions, four railway crossings and a parallel shared cycle and pedestrian path.
Stockport Council, along with its partners Cheshire East and Manchester City councils, are consulting on the road scheme in two phases.
The first phase of consultation on junction options comes to a close this month.
A second phase of consultation will take place in spring when the three councils will seek views on the preferred scheme, prior to the submission of a planning application in summer.
Prequalification information is available at the Chest Portal.