The Spanish international has two years left on his contract at Arsenal, with a one-year extension option built-in.
According to the 'Daily Mirror' the player's desire to leave is not particularly strong, but Unai Emery doesn't have any especially exciting plans for him in the coming season.
Real Sociedad have recently lost Alvaro Odriozola to Real Madrid for a deal in the region of €30million, and Monreal could now be in their sights.
However, it looks like it could be a hard sell to get Monreal to leave the Gunners.
However, reports from Spanish outlet 'AS' suggest that Sociedad have already made contact with Monreals representatives.
In the coming few weeks it will be clear if Monreal will be lured back to his country, or if he will stick with the Gunners.