Traore was expected to join Juventus, but the Daily Express now reports that Galatasaray and Liverpool are chasing the 23-year-old striker.
Traore's agent, Dmitry Selyuk told Izvestia: "Recent developments have not changed Traore's relationship with Anzhi.
"Moreover, he believes that the change of direction towards development will benefit the club.
"He loves to work with [new coach] Gadzhi Gadzhiyev, who has assured him that he counts on Lacina as the main striker.
"But I can't deny that in the case of a decent proposal that suits both us and Anzhi, Lacina could still change club.
"The interest in Traore in Russia and Europe is quite large.
"Therefore, if we get a good offer in the winter I think the leadership of Anzhi will let him go.
"But there are not many teams that could afford to pay the price for the player."