The manufacturers - which are grouped under the banner Grand Prix World Championships (GPWC) and include Fiat, Ford and DaimlerChrysler - have shortlisted three agencies to pitch for the work, which is set to cover the UK, France, Germany and Italy.
Hill & Knowlton is one of the agencies to get through to the second round of the review, which is being conducted by GPWC's recently appointed investment bank Goldman Sachs.
The successful agency will help GPWC devise a strategy for dealing with PR surrounding the breakaway issue and mounting tension with motor sport regulator Federation Internationale de l'Automobile (FIA).
GPWC is negotiating the purchase of a controlling stake in F1 and is threatening to form a rival group if its bid to get control over the existing racing programme fails.
According to a Goldman Sachs document obtained by PRWeek, GPWC is looking for strategic PR advice on the group's interaction with the FIA and what 'tangible steps GPWC could take to improve the situation from a PR perspective'.
The brief will also include media relations, in terms of general, financial and specialist sport media.
F1 manufacturers have been angered by recent rules brought in by the FIA, which were aimed at reducing development costs facing F1 teams.
The top racing teams - Ferrari, McLaren and Williams - have been vocal in objecting to the changes, which they claim will dumb the sport down and make F1 racing less safe.
News of the GPWC pitch follows the appointment of Brunswick by McLaren and Williams to help represent their interest and address concerns over safety.
Brunswick partner James Hogan is leading the brief, reporting to Williams principal Sir Frank Williams and McLaren MD Ron Dennis.