Thauvin is out of contract in the summer and is now unlikely to sign a new contract with Marseille to stay at the club, as he edges towards leaving the Stade Velodrome.
The Frenchman held talks with several clubs in Italy and he was also linked with a move to the Premier League in the summer.
Crystal Palace and Leicester City were believed to be interested in him, but it appears he had an offer from the London Stadium.
According to French sports daily L’Equipe, West Ham wanted to sign the former Newcastle winger and made a proposal to the player.
But Thauvin turned down the chance to move to the London Stadium and is now set to move to Mexico.
He has agreed on a five-year contract in principle with Mexican outfit Tigres, but is yet to sign on the dotted line.
The winger is still expected to formally complete his shock move to Mexico.
