Arteta has been sidelined since suffering a knee injury against Newcastle United in February, while Jagielka has been out since April after picking up a similar problem against Manchester City.
Moyes is also without Victor Anichebe and Phil Neville due to long-term injuries, and the Toffees chief hopes the bulk of his players will be back next month.
"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."
UnnoticedMeanwhile, Moyes believes Everton's achievements in recent seasons continue to miss out on recognition due to the money spent by other clubs.
He added: "I think (Manchester) City have a great chance of winning the league. I have said that before, and I think Tottenham and Aston Villa will be in there as well. And they should all be talked of in that breath because of their finances.
"I think if I had spent that money I would have had a feeling I should be trying to achieve that position.
"But, considering where we are, I think that sometimes we go a little bit unnoticed.
"We have come fifth in the last two years and I don't think anyone has really said anything about Everton."