It is understood that the review is being overseen by AAR and is a separate piece of business to an Amazon UK retail brief already reported to be in play.
Mischief, which looks after the LoveFilm movie rental service, and Cult Brand, which covers the MP3 service, had not responded to requests for comment at the time of publishing.
AAR and The Red Consultancy, which handles work on the Kindle tablet as part of a wider UK PR brief that is thought to be unaffected, both declined to comment.
Amazon, which has not responded to a request for comment, generated global sales of $17.1bn (£10.4bn) in Q3.
According to analysts Experian, Amazon attracts 12 per cent of visits to retail sites in the UK, second only to eBay.
However it recently faced criticism in a BBC documentary in which a stress expert claimed working conditions at its UK distribution centres could cause "mental and physical illness".