Traore was one of the Championship's standout performers this past campaign, and could be difficult for Boro to hold on to after their play-off elimination at the hands of Aston Villa, the Spaniard's former club.
However, it is claimed Traore could command a fee 'in excess of £30 million' should Tottenham choose to pursue a deal, with Chelsea also listed as suitors.
The 22-year-old comes from good stock, having progressed through Barcelona's youth system, but has taken time to find his feet in English football.
Former Spurs boss Tim Sherwood was first to take the plunge, paying a reported fee of £9 million to bring him to Aston Villa, who later part-exchanged Traore for Albert Adomah.
Traore showed glimpses of his ability last season, as Middlesbrough slipped out of the Premier League, and excelled with five goals and 10 assists from 28 league starts in 2017-18.
Tottenham may have to offload one of their current wingers in order to accommodate the former Spain Under-21 international, with returning loanees Josh Onomah and Georges-Kevin Nkoudou perhaps the prime candidates.
Should Tottenham move for Middlesbrough's Traore this summer?