Aubameyang left Arsenal under a cloud in January after being dismissed as captain and having his contract mutually terminated.
The Gabon international ended up joining Barcelona but is now linked with a sensational return to English football with Chelsea.
Blues boss Thomas Tuchel previously worked with Aubameyang at Borussia Dortmund and remains a fan of his talents.
And asked if Aubameyang would be given a good welcome on a possible return to the Emirates, Arteta said: “I hope he does because I think he deserves it.
“There are times in life, there are times in your career, and sometimes every individual’s trajectory or goal is different from clubs – and you have to respect that.
“Auba is an exceptional player. He did so much for us. He was our captain and I think we have to be grateful, very grateful too, for what he did for this club.
The fallout of Aubameyang leaving Arsenal has been in the spotlight this week as it is covered in episodes four and five of Amazon Prime Video’s on-the-fly documentary series ‘All or Nothing: Arsenal’.
During the episodes, it is revealed that Arteta had a “catalogue of offences” regarding Aubameyang and technical director Edu describes the couple’s relationship as “zero” at one point.
“Look, it’s been a long time since that happened. I can’t go back every time there is another series,” added Arteta. “I made my comments on that, I was really clear and honest with my opinion.
“What has been done has always been done to defend our club and put it in the best possible position, and always being as clear, honest and consistent as possible.”