Carillion and Hochtief have been shortlisted as sole bidders, while Graham / Farrans and Sisk / Lagan Construction Group joint ventures also make the list.
Work will start this autumn and is expected to take two years to complete.
The new 7.5 km bypass will link the A158 Wragby Road roundabout to the A15 at Bracebridge Heath.
The shortlisted contractors will be encouraged by Lincoln County Council to subcontract parts of the work to local SMEs.
The controversial project was given the green light by the Department for Transport in February following two public enquiries that saw hundreds of local residents object to the plan.
Lincolnshire County Council executive member for highways and transport Richard Davies said: “Each of the four companies shortlisted for the two-year contract will now be looking at the finer detail in their submissions, which will include the need to subcontract some of this work out to smaller companies.
“I would urge any local company interested in this work to put their hand in as soon as possible by contacting the four companies direct.”