The government department contacted agencies last week in a process being run through the Crown Commercial Service. The pitch is open to shops on the government roster.
The business is currently handled by Engine, which has worked on HMRC activity since 2012, when it picked up a range of ad-hoc projects.
Engine gained the ad account the following year after seeing off competition from seven other agencies. WCRS, Engine’s creative shop, has created campaigns including "Inner peace" for self-assessment, which explained how relaxed people felt after submitting their tax returns.
The Crown Commercial Service reviewed its roster last year. Engine held on to its place but Abbott Mead Vickers BBDO and McCann lost theirs.
A spokesman for HMRC said: "We are looking to work with an agency on a three-year, fixed-term contract, which will start in August."