Arsenal are believed to have led the chase for his signature since it emerged that they were considering an approach, with the player favouring a switch to Emirates Stadium.
Discussions regarding a transfer to England have been opened, but slow progress is being made at present.
Lille, though, expect an agreement to be thrashed out, with Seydoux resigned to the fact that Gervinho will soon be on his way to pastures new.
"We know that Gervinho has a personal interest in joining Arsenal," he told RMC.
While one forward-thinking player appears set to depart Lille, Seydoux has again moved to play down rumours regarding Belgian starlet Eden Hazard.
PromisesThe youngster continues to be linked with a number of top clubs, with the recent takeover at Paris St Germain seeing them join the hunt.
Seydoux, though, insists Lille have no intention of parting with the talented 20-year-old.
He said: "Even if big money is offered, my answer will still be the same. Eden stays here.
"They say things can change very quickly in football, but at Lille we keep our promises."
Seydoux has also confirmed that he is hoping St Etienne forward Dimitri Payet can be lured to Lille, despite mounting interest from PSG.
"We know there is competition," he said.
"With Payet, many agents are talking. We will have to see what the player wants."