The Descendants actor will produce and star in the upcoming film, reports Variety.
The project will also reunite Argo writer Chris Terrio and producer Grant Heslov with Clooney, who produced the recently-released drama starring Ben Affleck.
The project is in development with Sony Pictures under Clooney and Heslov's Smoke House banner.
Further details of the project remain scarce.
Greengrass's next feature Captain Phillips will debut in October 2013.
Clooney will next be seen starring opposite Sandra Bullock in Gravity.