According to the report, the winger’s representatives met West Ham officials at the end of last week, and that the deal could be completed later this week.
The 21-year-old winger joined Middlesbrough from Aston Villa in the summer of 2016, but the youngster failed to make an impact at the Riverside Stadium.
During the 2016-17 season, Traore failed to score a single goal and provided only one assist in 16 Premier League starts for Middlesbrough.
Back in 2015-16, the former Spain Under-19 international failed to score and created only one chance in 10 Premier League appearances for Aston Villa.
West Ham endured a disappointing 2016-17 Premier League campaign and will be aiming to push for the top six next season.