The Mexican left the Premier League side on a permanent deal last summer after failing to force himself into Arsene Wenger’s first-team, despite being in north London since 2005.
Since his arrival in Spain, the 24-year-old has been impressive, helping Real Sociedad move into fourth place in La Liga, and give themselves a chance of Champions League football for next season.
Upon his sale, the Gunners inserted a £4m clause allowing them to bring back Vela should they choose to.
His fine performances have alerted Wenger, who is now exploring the possibility of bringing the man he saw as surplus to requirements back to the Emirates Stadium.
The only issue remains Vela’s willingness to return to Arsenal.
He is believed to be enjoying life with the Basque outfit, and could be reluctant to move back to surroundings in which he failed to find his feet.
However, Arsenal may be able to tempt him back with his chances of playing regularly at the highest level much increased in London.
Arsenal are also believed to be keen on Vela’s team-mate Antoine Griezmann.
The 22-year-old Frenchman is widely thought of as one of the finest talents in La Liga, and has made over 100 appearances for Real Sociedad despite his youthful age.
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