The Turkish sports newspaper report that the Black Eagles have been keeping close tabs on the Canadian international and that his fellow compatriot Atiba Hutchinson who plays for Besiktas has acted as an intermediary in the initial talks.
Hutchinson has established himself as one of the star players in the current Besiktas side and is reported to have been working on convincing Hoilett to join.
The Eagles could sign the 25-year-old winger on a free transfer as he has under six-months remaining on his current deal.
The Istanbul giants were also linked with Hoilett last summer but were unable to prize him away from West London.
Hoilett joined QPR from Blackburn Rovers back in 2012 and has six goals and two assists in all competitions for the Hoops this season.
Besiktas would be able to offer Hoilett Champions League football next season and are currently first in the league five points ahead of second placed Fenerbahce.