According to Ghanasoccernet, officials of the Super Lig side granted him permission to leave their winter training camp in Antalya.
Family sources say Gyan has not spoken to his wife or three children since August, even at Christmas when he usually visits, and his kids are understood to be getting worried about their dad’s whereabouts.
Gyan is not returning calls - it is unclear whether that is out of choice or not - and is awaiting DNA tests to confirm their identity.
However, Gyan is expected to join Kayserispor’s camp before the end of the camp.
He is likely to meet up with the team in the city of Kayseri.
The former Sunderland striker, who earned A$408,000-a-week at Shanghai SIPG between 2015 and 2017, is understood to have just $1000 in his bank account and is unable to provide for his family.