Liverpool are thought to be in the market for a new striker when the transfer window reopens in January, with Brendan Rodgers short of attacking options at Anfield.
The Reds failed to bring in a replacement for Andy Carroll during the summer transfer window and with Fabio Borini injured, Luis Suarez is the only recognised senior striker available to Rodgers.
Traore is now thought to be on Liverpool's radar after impressing for Anzhi against them in the Europa League clash last week.
The giant Ivory Coast hit-man scored the winning goal in Thursday's Europa League tie and Traore's representative, Dmitry Selyuk, claims Liverpool are leading the race ahead of Udinese to sign the 22-year-old.
"Aside from Liverpool, Udinese are another on the list of clubs to have made contact about the purchase of Traore," Selyuk, told Izvestia.
"I'm afraid the Italian side won't be able to meet the player's valuation."
However, Selyuk claims Traore is in no rush to leave Anzhi for Liverpool.
"At the moment Lacina is happy with his situation at Anzhi," Selyuk added. "Not long ago he signed a new contract until June 2016.
"There's no reason for Traore to rush."