Group comms manager James Bailey confirmed a pitch was underway, as the company plans to hire one agency to handle a combined PR account.
A shortlist has not yet been drawn up but a decision is expected by the new year.
Goodyear and Dunlop formed a 'strategic alliance' three years ago but since then have continued to use different agencies for PR work.
Dunlop has retained West Midlands-based McCann-Erickson for PR for more than ten years, while Goodyear has used Hill & Knowlton for pan-European special projects, including UK work.
Bailey said McCann-Erickson was one of three agencies with which it had already had discussions.
Bailey said the decision to stage the pitch was no reflection on McCann-Erickson's past work, stating 'it is a very different brief now', and stressing that the desire to closer co-ordinate the Dunlop and Goodyear brand initiatives lay behind the pitch process.
In September Goodyear and Dunlop moved into a new joint headquarters - TyreFort - in Birmingham. This co-location is part of a plan to better integrate the two companies.
Bailey said it was most likely the hired agency would be based in Birmingham or at least have an office in the city.
Bailey said the companies' PR work targets audiences ranging from car and truck-rental fleets to garages, motorsports enthusiasts and agricultural users and truckers.