The 25-year-old made a permanent switch to the Spanish outfit in 2012 but the Gunners included a buy-back option which they could to activate to beef up their threadbare attack.
Aperribay revealed the talks between the two clubs about the striker, who netted 21 times in all competitions for the San Sebastian outfit last term.
“Arsenal have told us they are interested in the player (Vela) and we have to think on that,” he told Euskal Irrati Telebista.
“The player wants to continue here, in San Sebastian, and this is an important point for us.”
The Sociedad head honcho also admitted to the difficulties they face in retaining their best players, with goalkeeper Claudio Bravo being tracked by Barcelona.
“We are talking with great clubs like Barcelona and Arsenal. Things are really difficult, but nothing is finished,” he added.
“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.
“Bravo wants to join for Barcelona, and you know there are advanced talks for him. I’m not going to talk about the price.”