Lille beat a host of clubs to his signature in January, after which point they allowed him to re-join his former club Bastia for the rest of the season.
Thauvin performed well for Bastia in the final few months of the season, and recently played a starring role in France's Under-20 World Cup win.
Marseille, along with the likes of Arsenal and Manchester City, have been strongly linked with Thauvin - but Seydoux is insistent that he will be staying put and making his debut for Lille this season.
"We know exactly what we want at Lille and I am stubborn. We will take our time for Florian to adapt to the group as we did in the past with Gervinho or Dimitri Payet," said Seydoux.