The Gunners sold their former flop forward to the Spanish side in 2012 on the back of a loan stint at the Anoeta, where he has since thrived.
But upon his move, Arsene Wenger saw a £3m clause inserted in the deal to bring the Mexican ace back at any time.
And after watching him fire Sociedad into the Champions League while helping establish them as a top La Liga club, the Frenchman is ready to give Vela another chance.
Arsenal are rumoured to be looking to test the 25-year-old during pre-season to see if he is up to the required level to boost their prospective Premier League title challenge next term.
Should he not be, they will then attempt to sell him back to a club in Spain for a profit, with the likes of Atletico Madrid and Valencia both keen.
Vela has already admitted that he would consider a return to north London, despite having endured a difficult spell in which he was frequently loaned out before being sold.