The Museum is currently undergoing a £20.5million redevelopment with new galleries, a learning centre and theatre expected to be opened in 2010.
Museum of London head of press and marketing Jo Fells said the deadline for interested agencies is 30 October, with an appointment expected before Christmas.
The appointed agency is expected to work closely with the four-strong in-house press team to provide support for the opening in Spring 2010. It will be expected to build anticipation and generate targeted media coverage in advance of the openings.