Vela joined Sociedad on a permanent deal from Arsenal last August, having spent the 2011-12 season there on loan after failing to cement a regular first-team place with the Gunners.
The move came after the striker, who joined the Premier League club from Guadalajara as a highly-rated youngster in 2005, took in three other loan spells during his time at Emirates Stadium.
Reports surfaced this week that Arsenal manager Arsene Wenger could take up a buy-back clause in the Mexico international's contract after seeing him rediscover his form in Spain this season.
The 24-year-old has scored 12 goals in 27 appearances for Sociedad this term as they push for a UEFA Champions League spot.
But while Vela remains grateful for the opportunity given to him by Wenger, the frontman insists he is happy in Spain.
He told Spanish news international agency EFE: "Arsenal are a big team who gave me the opportunity to play in Europe. I will always remember that, but I didn't have the opportunities that I felt I deserved.
"I am here (at Real Sociedad) and would like to stay here."