The striker has a year left on his current contract at the club and there have been reports that he is on the brink of committing his future to Arsenal, although there is yet to be official confirmation. Arteta believes that Aubameyang will put pen to paper.
The Spanish coach said: "We have had some really good talks with him and his agent and I am pretty confident we will find an agreement soon. That's my feeling."
The Gunners are also close to completing the capture of Lille defender Gabriel Magalhaes and Arteta is "positive" that he will join the club.
He said: "We can't announce anything yet, the deal is not finalised.
"He is a player we have followed for a long time and hopefully we can get it done. Sometimes in the final stages it is not as easy as it looks, but again we are pretty positive we can do it."
However, Arteta is less certain about the future of Dani Ceballos, who spent last season at the Emirates Stadium, suggesting that his parent club Real Madrid have control over his next move.
The 38-year-old manager said: "He was pretty clear with me that his intention was to remain with us but obviously Real Madrid is involved. I don't know yet what they want to do with the player.
"But he's a player that we are interested in because we really saw, in the last few months of the season, what he is capable of bringing to us."