The council is inviting contractors to prequalify to build the striking 336m span bridge, warning any upfront bidding costs cannot be reclaimed if the project fails to win funding.
More than 45 major transport schemes were last year included in the Government development pool to bid for a share of an available £600m funding pot.
Major transport projects like the Wear Crossing expect to hear whether they have won funding from the Department for Transport before the end of the year.
The Sunderland Strategic Transport Corridor project has been split into five separate delivery phases covering associated transport projects.
Today firms are being invited to pre-qualify for phase two. This involves constructing the landmark bridge over the River Wear and its associated approach roads to link it to the existing highway network.
Detailed designs have been developed by the council for the bridge, which will feature two independent curving concrete and steel composite masts, with stays supporting the deck from one side of each mast only.
Although the design of the bridge and the highway works will not form part of the proposed contract, the contract may include contractor designed elements of the works.
The contract may also include the construction of highway improvement works to Wearmouth Bridge southern bridgehead.
Should funding be granted, the project is expected to get underway next October, with it being finished by November 2015.
Contractors have until 1 December to express an interest. Pre-qualification questionnaires and associated documents can be obtained from the NEPO purchasing portal (www.qtegov.com).