The council is inviting firms to prequalify for an early contractor involvement role followed by a separate design and build contract.
Phase 4 includes dualling the A4440 between Ketch and Powick roundabouts, including Carrington Bridge over the Severn, a notorious bottleneck.
Welsh contractor Alun Griffiths began phase three works to reconfigure the Norton roundabout a year ago and is due to complete this winter. The firm also picked up the smaller £8m phase two contract which is now complete.
The council is aiming to award the ECI deal by February 2017.
Further information is available from the council procurement office.