The Wolves winger has put in some stellar performances in the first half of the Premier League season.
Traore's pace and unpredictability on the ball can be devastating, but he was criticised last season for a lack of quality final ball.
However, this season he has seemingly corrected his shortcomings and is delivering consistently effective shots and crosses to add goals and assists to his game.
Traore scored and assisted as Wolves defeated City last month and all but ended their title hopes.
Pep Guardiola has been outspoken of his admiration for Traore, fueling speculation that a summer move could be on the cards.
Liverpool are seeking exceptional talent to improve what is already a very polished side.
The Reds are understood to see Traore as offering something different to what they already have in the side.
The 23-year-old came through Barca's ranks as a youngster and the pull of La Blaugrana to former pupils has always proven strong.
Any club who wish to sign Traore will have to meet Wolves asking price, thought to be £70m or above.
Wolves will recieve the full fee for the Spaniard as his former club Middlesborough didn't insert any sell-on clause when they sold him for £18m.
Traore has five goals and seven assists in all competitions so far this season.
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