The up-and-coming architect, who was part of the AJ's 40 Under 40 last year, agreed to take on the project during a visit by its client to the UK in late February.
'Another Museum' will have around 16,500m 2of gallery space to house permanent collections of contemporary art from Asia, Europe and the US.
The gallery owner, Korean entrepreneur Kim Chang-il, is already rumoured to be collecting art with the new museum in mind.
A spokesperson for Adjaye's London office confirmed that the architect had been asked to design the scheme, but added that 'nothing is set in stone'.
The new gallery will sit next to Kim's existing Arario Gallery in the city of Cheonan, and will be part of a giant complex containing shopping malls, multiplex cinemas and restaurants.