The 33 year old has been on trials at the La Liga club for some weeks now and according to reports the former UEFA Champions League semi finalist are set to hand the Ghanaian a contract.
The hard tackling midfielder has been without a club since terminating his contract with Saudi side Al Ittihad.
Having played for several European giants, including AC Milan and Inter Milan, Muntari's experience will be valuable to the La Liga outfit.
According sources close to the player, a contract to the end of the season will be handed to the player, who believes he is not yet done with the sport.
Muntari has been in the news for several controversies in the past but his recent campaigns against racism has been widely accepted and championed.
The player left the pitch in a serie A game following chants from Cagliari fans, when he played for Pescara.
Sulley Muntari's move to Deportivo will see him work with former AC Milan star Clarence Seedorf who was recently appointed manager of the club.