The report suggests that Slaven Bilic would be willing to pay £8million for the former Barcelona man as he looks to add some pace in wide areas.
While Traore has shown potential since moving to England two years ago and - according the Teesside Gazette - Boro do not need to sell him, the Championship club should jump at the opportunity to recoup a significant fee.
Traore enjoyed some fine performances last season, but, for all his talented ball skills his impact in the final third was negligible, serving up no goals and just one assist.
It was that lack of a killer touch that contributed to Boro's relegation, although they were willing to entertain a player who could offer a speedy outlet as they spent much of the campaign on the defensive.
Next season, though, it will be a different story. Boro have recruited Garry Monk and are SkyBet's joint-favourites for the second tier title, at 7/1 as of midday Saturday.
Monk cannot afford to rely on a winger who flounders in the final third as his side look to dominate matches. Boro have suffered in recent years for their lack of goal threat; they must not do so again.
If West Ham are willing to pay £8m, a move could suit all parties.