The 23-year-old Ivorian is wanted by a hoist of clubs and Rodgers would not get it all his own way with Juventus, Dinamo Moscow and now Turkish giants Galatasaray also being linked.
The player's agent, Dmitry Selyuk, says many clubs remain in the hunt to sign Traore but whether the Reds will make a move remains to be seen and much may depend on their league position in the New Year.
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."