The client - Maidstone council - wants the winning scheme to attract more visitors to the collection, which contains around 600,000 artefacts.
The initiative is for the East Wing and follows the Lottery-funded renovation of the West Wing, which was completed in 2003.
The full brief has three major elements:
the long-term preservation of the collections
greater public involvement in the Museum and its collections
increased use of the Museum and its collections.
Selection will take the form of a competitive interview organised by the RIBA Competitions Office. For further information, visit www.ribacompetitions.com
The deadline for expressions of interest is 19 September.