When Vela left the Emirates Stadium in 2012 a clause was placed in his contract allowing Arsenal the chance to bring him back to the club, and Arsene Wenger is keen to do so after he scored 16 goals in La Liga last season.
However, Sociedad are keen to hold onto the 25-year-old who has scored 35 times in his two seasons at the club, and president Jokin Aperribay insists they will do everything they can to ensure he remains at Anoeta.
"Arsenal have told us they are interested in the player (Vela) and we have to think on that," he told Cadena Sur.
"The player wants to continue here, in San Sebastian, and this is an important point for us.
"There are no discussions in this regard and therefore it is difficult to talk about whether we would be near or far.
"We will see in the near future if we go a little and accomplish something for Real."
Vela originally joined Arsenal at the age of 16 and made 60 appearances in all competitions for them, scoring seven goals.
