The four-year contracts are worth £4 million a year for advertising, £5 million for direct marketing and £4 million for brand strategy and services.
The review is being handled by Tom Hings, the Royal Mail director of brand marketing.
The winning agencies will have to overcome negative public perception caused by the ongoing dispute over pay and pensions that has seen walkouts and stoppages by Royal Mail staff over the past two weeks.
Earlier this year, the Royal Mail handed its media account to OMD UK. The agency picked up the business following a pitch against PHD, MediaCom and the incumbent, Carat, which had held the account for ten years.