A monetary policy decision is due on December 27.
President Gotabaya Rajapaksa will make the appointment following a recommendation from the Prime Minister who is the finance minister.
Senior government officials had earlier indicated that a decision would be made over the weekend.
In the absence of a governor, the most senior deputy governor overlooks the central bank, who is currently Nandala Weerasinghe.
Weerasinghe is also among candidates to be appointed governor.