The 23-year-old has struggled to impress in England since joining Arsenal in 2005, but he has scored seven goals in 26 games on loan for Sociedad this season.
He is due to return to England at the end of the season, but Aperribay has claimed that the Spanish club are keen to discuss a permanent deal.
"It is true, we want the player and we are prepared to fight to close the deal. At the moment things have stopped because Arsenal only want to speak at the end of the season. It will not be easy, but Vela wants to stay here and that could be crucial in the negotiations," Aperribay told Sky Sports News.
Vela has 35 Mexican caps to his name.