The 20-year-old winger has been linked with a move to Stamford Bridge with Antonio Conte said to be considering a bid this month.
Traore has made eight league starts for Boro this season without scoring but has caught the eye with his electric pace and skill.
Diego Costa snapped training on his own at Chelsea
Mon, January 16, 2017
Express Sport brings you all the best snaps as Diego Costa is pictured training on his own at Chelsea
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Diego Costa has been pictured training on his own
Aitor Karanka wants Adama Traore to stay at the Riverside
Yesterday, Patrick Bamford made the permanent move from Chelsea to Teeside.
And Karanka wants Traore to remain alert with the increased competition now at the club.
Adama Traore holds off Nathaniel Chalobah
"If a team like Chelsea is following Adama, it's because his progression has been brilliant in six months and he's doing well,” he said.
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"But he's young and the main thing he has to do is to keep going in the same way because football changes a lot.
"Maybe he is in a big moment, but with Patrick here now, with other players already, maybe in two or three months, he will not be playing and Chelsea disappears and everybody disappears."