Sky Sports says Istanbul Basaksehir are keen on signing Taylor.
The 32-year-old is a free agent this summer as his deal at Villa Park expires.
And the Welshman is attracting plenty of interest from abroad including clubs in Qatar and Saudi Arabia.
Basaksehir are the latest side to enter the frame, with their Turkish rivals Trabzonspor also interested.
Villa could still offer him a new deal but are waiting until the end of the season to make a decision on his future.