Chelsea have previously shown an interest in the speed demon, though the player's inconsistent start to the season under Garry Monk, which often saw him left out of the side, coupled with Middlesbrough's refusal to sell put clubs off.
Since the arrival of Tony Pulis in December, Traore has come on leaps and bounds, scoring five goals and providing eight assists since the turn of the year as he established himself as one of the hottest properties outside of the Premier League.
Traore's raw pace and ability to beat a man is unparalleled in the footballing world and the 22-year-old has "all the attributes" to make it at the top level, according to Pulis.
A source close to the player told 'the Mirror': "Adama knows there is major interest – and Chelsea have always been at the head of the queue."
Newcastle and West Ham have made their interest known in the past, but both would be unable to compete with the 'Blues'.
Nevertheless, Middlesbrough remain reluctant to sell and having secured a play-off place, the club are hoping that promotion could convince the former Barcelona academy star to commit to one more season at the club.