Requests for information have been sent out to agencies and the pitch process is being handled by intermediary Agency Insight.
The7stars currently handles the organisation's regional media planning and buying, which is not thought to be affected by the campaign.
Last month, the National Trust rolled out a new strapline - "time well spent" - to promote value for money and simple pleasures.
The ad campaign, which was created by MBA, runs until October and promotes National Trust properties across the national press, outdoor and online.
The Trust, with 35 million members, protects more than 300 historic houses and gardens, as well as 49 industrial monuments and mills.