The 24-year-old, who made his move to Real Sociedad permanent last summer, reportedly has a clause in his contract which would allow the Gunners to re-sign the attacker at the end of the season.
However, he has insisted that he wants to remain at Sociedad, who currently occupy fourth spot in the La Liga table.
"Going back to Arsenal? It could happen at any moment, but I don't want to think about it," he told L'Equipe.
"My life is at Real Sociedad, and it is with that shirt that I want to play in the Champions League next season."
Vela has scored 13 league goals for the Spanish club this season.