The Gunners are keen to bring the Mexican back to North London, though the striker hopes to remain in Spain.
The Mexican striker made the switch to the San Sebastian outfit in 2012, though the Gunners included a buy-back clause in his sale that allows them to re-sign Vela for a fee of just 4 million euros.
While Sociedad is keen to keep both the 25-year-old striker and goalkeeper Claudio Bravo — a target for Barcelona — Aperribay acknowledges the club could lose the pair, even though Vela would prefer to stay.
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"We are talking with great clubs like Barcelona and Arsenal. Things are really difficult, but nothing is finished," he told Euskal Irrati Telebista. "We are in a difficult moment if we want some players to continue at Real Sociedad next year, but we'll try to complete our squad in the best way. We understand what Arsenal represent and what Barcelona represent. There aren't deadlines with them, just talks, and we are looking at what is best for us.
"Arsenal have told us they are interested in the player [Vela] and we have to think on that. The player wants to continue here, in San Sebastian, and this is an important point for us.
"Bravo wants to join for Barcelona, and you know there are advanced talks for him. I'm not going to talk about the price."