The Mexican attacker left North London on a permanent basis in 2012 after slipping down the pecking order at the Emirates Stadium under Arsene Wenger.
He has since thrived with Sociedad – whom he was with on loan before signing on a full transfer – becoming a first-team regular as they secured qualification for the Champions League last season.
His displays have seen attention from a number of European clubs rise, including Arsenal.
When allowing him to leave the club they had a £4m buy-back clause inserted into the deal, which could be activated to secure his return.
With Wenger currently short on attacking options, it is understood that this has become appealing ahead of the next transfer window.
However it remains unclear as to whether or not Vela will be open to a return to the club.
The pacey star spent a largely unsuccessful seven years with Arsenal, during which time he frequently moved away on loan.
Despite his struggles at club level, Vela has earned 35 international caps, yet he is not expected to represent Mexico at the World Cup after opting out of a number of recent squads.