Last summer, Traore signed a long-term contract with Middlesbrough but they are likely to receive offers for the pacy attacker following the North-East outfit's relegation from the Premier League.
According to Gazette Live, West Ham boss Slaven Bilic has identified Traore as a potential signing and is willing to place an £8m bid for his signature.
In January, it was claimed that Chelsea were prepared to pay double that amount to take the 21-year-old to Stamford Bridge but after he ended the season having failed to score in 31 appearances, he may be available for a lower fee.
However, Middlesbrough do not need to make sales in order to balance the books, and it appears that the decision over his future will lie with new boss Garry Monk.
The former Barcelona trainee initially cost Aston Villa a fee of £7m when he arrived in 2015, before his switch to the Riverside Stadium 12 months later.