The Barcelona striker is being linked with the Blues this week.
Arteta said: "Auba is an exceptional player, he did so much for us. He was our captain and we have to be grateful, very grateful for what he did for this club."
"I'd hope he does because I think he deserves that. There are moments in life and there are moments in your career - sometimes the trajectory and objectives of each individual are different to the club's. We have to respect that.
Arteta was also quizzed about whether Chelsea had asked him for his 'file' on Aubameyang.
He replied: "Auba is an exceptional player. He did so much for us - he was our captain and we have to be very grateful for what he did for this club.
"It's a long time since that happened. I cannot go back every time there is another series. I have made my comments on that. I was really clear and honest with my opinion and what has been done has only been done to defend our club and put the club in the best possible position while being as clear, as honest and as consistent as we can be."