Graeme Souness is a big fan of the young Frenchman and has gone back to test Gerard Houllier`s resolve after having two previous bids rejected.
The player himself is very highly rated at Anfield, but the lack of first team opportunities for the 21-year-old may see him get a move.
Houllier paid £500,00 to Laval for his services in February 1999, but he has started just eight games as Jamie Carragher cemented himself into the left back position.
Traore signed a new contract in December, but Souness remains hopeful that he can lure the youngster to Ewood Park.
Rovers have also lodged a bid for Birmingham`s Martin Grainger, but Traore is Souness`s first choice.
