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The 27-year-old has entered the final two years of his current deal, which he signed when joining the club for £105million in the summer of 2023.
Talks over a new contract began earlier this year and there has always been confidence on both sides that an agreement will be reached.
It is understood that Rice is close to signing that deal, one that will earn him a significant salary increase and take him close to Bukayo Saka on £350,000-a-week as the club's best-paid player.
Official confirmation of that extension has not yet come but Arteta is in no doubt that a positive outcome will be reached.
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.
Rice played 69 matches for club and country last season in a remarkably intense campaign.
He was managing neural pain in his hamstring for much of that period and played through the pain at the World Cup over the summer.
Despite that workload, Rice returned to start his pre-season after only three weeks off and has been straight back into the action.
The midfielder has started all eight of Arsenal's Premier League matches this season and he is expected to play a key role when the Gunners travel to Anfield to face Liverpool on Sunday.
"What we are demanding him to do, every year, is very difficult to maintain. He's doing it, big credit to him.
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"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."