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Rice joined Arsenal in 2023 for £105m, but is currently in the final two years of his deal.
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Talks started with the England international at the start of the year and there was always confidence he would extend.
Asked if he is expecting talks to be finalised soon, Arteta said: "Yeah.
"My feeling is that he is very happy here. Every conversation that I have with him, he wants to continue here for the long term.
"It will be a matter of time when we resolve that."
Reports suggest Rice will be paid in the region of £350,000-a-week, a significant increase from the £240,000-a-week he gets currently.
This would put him on a level with Bukayo Saka as the best paid player at Arsenal.
Manager Arteta earns a basic salary of £20m-per-year, which equates to around £384,000-a-week.
The Gunners boss himself signed a lucrative long-term contract until 2030 in October.
Speaking on Weekend Sports Breakfast, journalist Jamie Jackson said: “It's obviously a great sort of re-signing, renewing of contract for Arsenal. He is kind of the fulcrum for the side.
“I think he's a heck of a player. He could probably score more goals if he asked me my opinion of where he could improve.”
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Rice has started all eight of Arsenal's Premier League games this season.
That will become nine on Sunday as the Gunners travel to Anfield to face Liverpool.
Arteta's side can go top-of-the-table if they get at least a point in the 4.30pm kick-off.
"I think he's (Rice) been very consistent again," Arteta said.
"What we are demanding him to do, every year, is very difficult to maintain. He's doing it, big credit to him.
"Big players for big matches and we know the kind of performance we need from Dec and the rest of the boys to get away from there with three points."