The on-loan Atletico Madrid star suffered the injury in Kayserispor's Turkish Super Lig game against Besiktas early last month.
He was expected to be out for six weeks but the attacking midfielder has started personal training under the supervision of the medical team of the club.
Mensah will join the rest of the squad for training next week.
The 24-year old has been an influential figure for the Kayseri club after making 22 appearances and scoring three goals for the club.
It is understood President of the club has opened talks with the Spanish giants on making the loan move a permanent one.
Kayserispor have struggled without the talismanic Ghanaian, winning just a game since he sustained the injury.
His return from injury is seen as boost for coach Kwesi Appiah, who invited him for the double header against Kenya and Mauritania only for the player to be replaced later due to the setback. Read Full Story