Rovers chief Graeme Souness has already tabled two bids, believed to be around the £3 million mark, for the French Under-21 international but Liverpool have shunned both offers.
Reds coach Gerard Houllier believes the left-sided defender, who has only played eight times for the Merseyside club, can fulfill his undoubted potential and has so far resisted all overtures from Ewood Park.
Liverpool legend Souness now seems unwilling to become involved in a bidding war for the French starlet and hinted that he may look elsewhere.
"We have made two offers now for Traore and I don't know whether we will be back in.
"Liverpool have turned us down flat with the two offers we have made so I don't know if there is any room left to maneouvre.
"He is a young player with terrific potential and he would be a good addition to our squad. At the moment, the whole thing is on ice," said Souness.
