The museum has contacted agencies with a brief to promote its individual exhibitions targeting families. The pitch is being handled by the AAR.
Chemistry meetings will take place in two weeks' time, with a final decision expected in early June.
The museum is looking for agencies with experience of working with entertainment venues. Isobel, the last agency to work with the museum, is expected to repitch.
The chosen agency will work alongside the museum's in-house creative team to create campaigns across press, outdoor and online.
The museum's last full pitch for the account was in 2005. Soul, Hooper Galton, Leith London, HOW, Isobel and Karmarama were shortlisted, but the pitch was called off a month later. Isobel has since handled the business on a project basis.
The agency's last high-profile campaign for the Natural History Museum was to promote its "ice station Antarctica" exhibition. It featured three children dressed up as Antarctic scientists, clad in explorers' uniforms with frosted beards.
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