The 20-year-old joined the French outfit from Bastia at the expense of a whole host of clubs in the January transfer window, including Arsenal.
Having impressed on his return loan to Bastia and during France's U20 World Cup win, Thauvin is again attracting interest from rival clubs, but Seydoux is adamant that the player will not leave the Stade Pierre-Mauroy.
"We know exactly what we want at Lille and I am stubborn," Seydoux told reporters.
"We will take our time for Florian to adapt to the group as we did in the past with Gervinho or Dimitri Payet."
Thauvin is yet to earn a senior cap for France.