Per the source, the Lions will offer City a €1 million loan-fee and Kolarov a €2m wage packet for the session.
City are reported to be open to offers for Kolarov and Besiktas were closely linked with the full-back until the recent troubles in Turkey unfolded.
The Black Eagles have now diverted attention to Barcelona full-back Adriano who is currently in Istanbul set to undergo his medical.
Besiktas would be unlikely to sign Kolarov if the Adriano deal goes ahead which would make Galatasaray’s job of convincing him easier.
Unlike Besiktas, Galatasaray will not play Champions League football as they are currently serving a one-year European competition ban for breaching FFP regulations.
Galatasaray are coming off the back of a disappointing league campaign but did win the Turkish Cup last season beating rivals Fenerbahce in the final.