Vela has been out of favour at the Emirates Stadium for some time and has not played for the Gunners since January last year.
After a spell with West Brom last season the Mexican international has spent this season on loan with Sociedad, who have been impressed by his talents and are ready to end his Arsenal nightmare.
The 23-year-old his the La Liga outfit’s leading scorer with ten goals to his name this season, and AS reports that his performances and goals have been enough to prompt them to approach Vela’s agent, Eduardo Hernandez, to set the wheels of a deal in motion.
Vela is out of contract next summer and Arsenal are keen to recoup any fee they can for the former Guadalajara forward before he is able to walk away for free.
Spanish newspaper AS reports that a bid of around £2 million will be enough to persuade Arsenal to part company with the Mexican international.
A permanent move to Sociedad would put an end to a frustrating spell in north London for Vela, who the Gunners held in high regard when he signed on the dotted line back in 2006.
Vela, who has also had loan spells with Osasuna and Salamanca, has played just 29 league games for the Gunners, the majority of which were as a substitute, although he has feature more regularly in cup competitions.