The 22-year-old has enjoyed a fruitful season for Boro, scoring five goals and registering 10 assists to help steer his side into the Championship playoffs.
Traore was linked with a switch to Stamford Bridge in January 2017 but a move failed to materialise, Boro subsequently suffering relegation from the Premier League.
According to The Mirror, the Blues have rekindled their interest in the Spain Under-21 international, with Tony Pulis facing a fight to hold on to his star man even if Boro return to the top flight.
The report goes on to claim that a deal, believed to be in the region of £30m, may be eased through as former Chelsea chief executive Peter Kenyon is a close confidant of Middlesbrough chairman Steve Gibson.
Traore, who has previously played for Barcelona and Aston Villa, is also believed to be on the radar of Everton and Newcastle United.