Rice was taken off in the 62nd minute of Arsenal's frustrating goalless stalemate with Everton in the Premier League last weekend.
Arteta revealed at his post-match press conference that the England international had asked to be substituted due to a niggle, raising concerns that he could face a short spell on the sidelines.
However, the Gunners boss has since offered an encouraging update on his No.41, confirming that he could feature in some capacity against Crystal Palace, pending a late fitness check.
Speaking to reporters on Tuesday, Arteta said: "He's fine, we'll make the decision whether he is available or not."
Zinchenko, Calafiori remain sidelined though injury
Meanwhile, Arteta has confirmed that defensive duo Oleksandr Zinchenko and Riccardo Calafiori "will still be out of the squad tomorrow" as they continue to recover from injury.
While Zinchenko has been absent from Arsenal's last three games due to a muscle injury problem, Calafiori has missed the last four matches with a knee problem.
Both players remain in the treatment room with fellow defenders Takehiro Tomiyasu and Ben White, the latter of whom underwent keyhole surgery to address a serious knee problem during the November international break and is facing several months on the sidelines.
Meanwhile, one other Arsenal player who is unavailable to play against Crystal Palace is on-loan backup goalkeeper Neto, who is cup-tied after representing parent club Bournemouth in the EFL Cup earlier this season.
Arteta: 'EFL Cup glory can open the door for further success'
Arteta is hoping to see his Arsenal side return to winning ways after two domestic draws, and believes that winning the EFL Cup could create a snowball effect for further success at the Emirates.
"I believe that if you are winning, it creates something different," Arteta told reporters. "These kind of games are really important. [Winning a trophy] is really helpful because it brings belief, trust and positive energy, touching the cup, and being in the semi-final and beating somebody in the final.
"It creates that energy and the right path to go and do something else, particularly because of the timing and when the competition is played in this country, it gets that momentum going.
"I fully believe in that, the fact that you are winning and you get into the next round and it creates something different around the team and that is why these kind of games are so important.
"We want to win and we will do everything we can to win it. The pressure is about being at a big club or winning the major trophies, and this is what we want to do."
Arteta has overseen just one trophy triumph in his Arsenal tenure - the FA Cup in 2020 - and his Gunners side currently sit third in the Premier League table, six points behind leaders Liverpool having played a game more.
Written by
Oliver Thomas