The Lions are expected to pay a €1.5 million fee for the services of Niasse on a one-year loan however, Everton are not expected to include a buyout clause option according to the Aksam newspaper.
Niasse is no stranger to Turkey having first made a name for himself at Akhisar.
The Senegalese international striker was coached by Hamza Hamzaoglu at Akhisar. The Turkish manager was later appointed Galatasaray manager and came close to signing Niasse but the deal stalled.
Niasse joined Lokomotiv Moscow instead before Everton snapped him up on a £13.5 million move.
Galatasaray have been in pursuit of a replacement striker since Burak Yilmaz joined Chinese giants Beijing Guoan.
The Lions will not be able to play European football next season due to serving a one-year UEFA ban for breaching FFP regulations.
The Istanbul giants had a disappointing league campaign but did manage to end the season with a trophy after winning the Turkish Cup.