But the 26-year-old has been unable to claim aregular starting place this term, when he fell well behind John Arne Riise and Stephen Warnock in the pecking order.
The imminent arrival of Valencia full-back Fabio Aurelio will further relegate Traore, while his chances of forcing his way in at centre-half are dashed by the signings of long-term prospects Daniel Agger and Gabriel Paletta.
Benitez will be hoping to attract adecent fee for a player who's acquired vast European experience since joining Liverpool in 1999.
Fulham and Everton have made bids for the versatile defender in the past, although it remains to be seen if their interest will be revived.
Manchester City also made an enquiry for the left back towards the end of the season, but Stuart Pearce has limited funds and is understood to be unwilling to meet Benitez's valuation.
Bolton are another club who've been linked with Traore previously, and Sam Allardyce is reported to have more money at his disposal this summer.
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