Rice is still battling a knee injury which forced him to miss the win against Aston Villa this week.
Asked if the swelling around his knee had gone down, Arteta said this morning: "Not yet, we have another session today, let's see how he comes today.
"Today will be the first training session with the players who started against Villa."
Pushed about whether he regrets playing Rice against Brighton, which saw him miss the Villa game, Arteta insisted: "No, no, no.
"He managed to do it. That's normal sometimes. You get a hit, and throughout the game you are able with adrenaline, and because you are warm, you are able to sustain that.
"And then the body reacts, and it reacted probably more than we expected, unfortunately. And that's where we are."
Alive in the market?
With the January transfer window now up and running, Arteta confirmed they would be seeking to buy this month. The Gunners manager says they believe it can be a market for opportunities, despite others writing it off.
He said: "We are open to finding a solution that is short medium or long, but let's see what happens and let's see the news in the next few weeks."
Arteta was also asked about Ethan Nwaneri's situation, with the teen struggling to force his way into the starting XI. It's been suggested the midfielder could be allowed to leave on loan this month.
Arteta said: "Every player is very important, that role can change for different reasons and every player has a role to play.
"We want to talk about peformance, not rotation. We have to play the best players in the best condition."
On the value of having Nwaneri available to come off the bench, he also said: "Well, very important and we don't know if a player will be a finisher or a starter. It's a joy because the players are committed and really willing to participate."
Opening up a gap
After Manchester City's draw at Sunderland, the Gunners now sit four points clear at the top of the Premier League table.
Asked about increasing the gap on the chasing pack, Arteta said: "It's where we are, we can always be better. The only thing that matters is Bournemouth."
On the energy and the ambition of his players, the manager said: "I think that's what they transmit every single day, you can see the desire how much they want it. Take it day by day, enjoy that process."
One player who typifies that approach is the in-form Leandro Trossard and Arteta enthused: "I think he's gone up every season. He's a player who really wants it, he's found his maturity here.
"We are very happy with him, we've talked about it many times and I think he's very happy here."
Before signing off, Arteta was asked for his reaction to Enzo Maresca and Chelsea parting ways on New Year's Day.
He concluded: "Wish him all the best, I really like Enzo. I think he's done a really good job at Chelsea, just wish him all the best."