It has contacted agencies with a brief to create campaigns that will target Londoners and encourage them to visit the attraction more often. The museum also plans to promote exhibitions and events taking place there throughout the year.
The chosen agency will work alongside the museum's in-house creative team to produce work across press, outdoor and online.
Chemistry meetings will take place later this month. A decision is expected in June.
The British Museum's first brand campaign was created in 2006. Handled by Brand Tacticians, it positioned the museum as a repository of the world's wisdom and a place to find inspiration.
One execution featured ancient Greek athletes giving workout tips and used the strapline: "Don't just look at our athletes, look like them."
The museum's media planning and buying account, which is handled by Total Media, is unaffected.