Aubameyang is out of contract in 12 months’ time and a new deal is yet to be agreed by the two parties.
The 31-year-old provided the Gunners with a timely reminder of his undoubted quality with two goals against Manchester City on Saturday to book an FA Cup final date with Chelsea on August 1.
Asked if there was a deadline for the deal to be concluded, Arteta told Sky Sports News: "I don't know, to put a date right now is very difficult.
"I like the way the conversations are going, I like what I'm hearing. I'm sure for both parties, the quicker we can do it, the better for everyone.
"I am confident he will extend his stay."
Arteta added: "He's generally happy. I think he is enjoying his football. He is settled in the country and his family are good.
"I think he can sense - and we've told him - how much we like him, how much we value him. I think the connection he has with the fans is unique. I believe he is in the perfect place for him.
"Everything I have from him and the people around him is the same. So I don't have any arguments to say something different."
Aubameyang has made 41 appearances in all competitions for Arsenal this season, scoring 25 goals.
Arsenal will face relegation-threatened Aston Villa in the Premier League later on Tuesday.