That leaves the Gunners with a major problems at left-back with summer-signing from Celtic Kieran Tierney still out injured.
Sead Kolasinac is being eased back after his training was interrupted when he was the victim of a gang attack.
Midfielder Granit Xhaka has even played played in the position this season.
And the right side isn't looking too healthy either.
Hector Bellerin is still crocked, Carl Jenkinson was sold in the summer and Ainsley Maitland-Niles seems more midfield than defence.
Monreal made 250 appearances for Arsenal, scoring 10 goals since joining from Malaga in 2013.
An Arsenal statement on the club website said: "We would like to thank Nacho for his contribution to the club and everyone at Arsenal wishes him the best for his future.
"The transfer is subject to the completion of regulatory processes."
Tierney and Bellerin are racing to be fit in time to face Manchester United next month.
The defensive duo have both missed the start of the season through injury - badly hampering Unai Emery's plans for his side.
But they are now on the verge of resuming full training with the rest of the Arsenal first team squad.
And the hope is they will provide a welcome boost by being fit enough to feature in the big match at home to top-four rivals United on September 30.
Tierney suffered his groin injury with Celtic before his £25million switch, while Bellerin has a long-running knee issue.
Arsenal fact Tottenham at the Emirates on Sunday in the mouthwatering North London derby.
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