Arteta has been out with a knee injury since February while Jagielka has been out with a similar problem since April.
Victor Anichebe and Phil Nevilla are also out with long-term injuries.
“I think November-ish is when we are looking at getting them back in,” said Moyes.
“Phil Jagielka is doing well and we would probably think about November with some luck, and Mikel is about the same.
“Even Victor Anichebe, too, who is important for us as another player.”