It is understood both Puma and the US firm held preliminary meetings with at least three UK consumer agencies last week regarding the work.
The pitch is likely to be one of many hosted by the sportswear firm worldwide, after realigning its PR function. Previously Puma used localised agencies, reporting directly to its in-house teams.
No-one from Puma in the UK was available to confirm details of the review as PRWeek went to press, but it is understood an appointment is likely within a fortnight.
Consumer PR for Puma was previously handled by Ketchum under its Ketchum Life brand, before being taken in-house last year.
The decision to revamp the firm's PR was taken to improve Puma's 'brand identity'. Global director of brand development Antonio Bertone said: 'We've been an amazing think-tank for new products but we've done a horrible job of telling people about that'.