The organisation is reviewing both its PR and public affairs work.
A document seen by PRWeek states that the PR work will include securing media coverage, crisis handling and social media activity.
The tender is open until the end of April and the incumbents are Equinox for PR and Positive for public affairs.
Public affairs work will include stakeholder engagement on both a local and national level and helping the organisation 'account effectively for its management of public and lottery funds'.
The NHMF was established in 1980 and has helped safeguard more than 1,200 iconic objects and places, including the Brecon Beacons in Wales and Wordsworth’s Dove Cottage in England.