The winner will develop a media strategy to increase membership and visitors to its properties across England, Wales and Northern Ireland.
MediaCom Direct is the incumbent agency. The review follows the appointment of MBA, which won the creative account from Craik Jones Watson Mitchell Voelkel in October.
Since then, the National Trust has split its potential customer base into different groups. The newly appointed media agency will be tasked with targeting customers through a number of channels, including direct marketing.
Charlotte Tams, the direct marketing manager at the National Trust, will oversee the pitch.
Since its appointment, MBA has produced press and DM campaigns that aim to promote the Trust's properties to a range of different audiences.