FEE is part of the Forestry Commission – which protects the UK's woods, forests and wildlife, provides grants to land owners and restores degraded land – along with Forest Enterprise Wales and Forest Enterprise Scotland.
FEE, which looks after 1,800 separate areas of woodland, is looking for one or more agencies to provide marketing and PR services and raise awareness of forestry issues.
The four-year contract will start in May this year.
Agencies have until the end of March to put forward proposals via the Government's Contracts Finder website.
The Contracts Finder website warns: "Travel may also include going to remote parts of the country and include outdoor visits in all weather conditions."