The 25-year-old sustained the problem - believed to be a broken toe - in last weekend's 1-0 defeat to Newcastle United and was unavailable for the showdown with Inter Milan in the Champions League on Wednesday.
Reports have claimed that Arteta will give Rice every chance to be fit for the trip to Stamford Bridge, where he would reunite with the club that he represented as a schoolboy from 2006 to 2013.
However, speaking to reporters in Friday's pre-game press conference, the Spaniard admitted that the midfielder was yet to return to training and is therefore running out of time to prove his fitness for the weekend.
"I have to be very vague on that one because there's no clarity on whether he's going to be fit for the weekend," Arteta said, before he was asked whether the reports of Rice suffering a broken toe are true.
"That's for the doctor, what I can say is that he hasn't trained yet and it is not clear whether he's going to be available or not to play," the Arsenal head coach added.
Will Mikel Merino, Kai Havertz be fit for Chelsea?
Double reunion in doubt? Arteta gives Rice, Havertz injury updates before Chelsea
With Rice unavailable for the clash with Inter, Mikel Merino, Thomas Partey and Leandro Trossard occupied the central positions at San Siro, but a nightmare evening for the former saw him denied a penalty at one end, concede one at the other and be taken off at half time.
Merino felt the full force of Yann Sommer's fists in the first penalty incident, which was waved away, before he was found guilty of a handball inside the Arsenal area, allowing Hakan Calhanoglu to stroke home the game-winning spot kick.
After Merino was replaced at the break, ex-Chelsea man Havertz was involved in a sickening clash of heads with Yann Bisseck and was left with blood pouring down his shirt as he departed late on.
Havertz did not appear to be concussed - rather he just suffered a nasty cut - but Arteta was customarily tight-lipped on the pair's fitness as well, adding: "We'll have to wait until tomorrow to see how they react.
"Kai had quite a nasty cut and he could not continue. With Mikel, to be fair the day before he wasn't feeling great and we decided to sub him at half time."
Is Martin Odegaard available to start against Chelsea?
Amid the fresh concerns for Rice, Merino and Havertz, Arsenal received one piece of good news in midweek, as Martin Odegaard was fit enough to come off the bench in added-on time following his severe ankle injury.
Asked whether the Norway captain was an option to start on Sunday, Arteta replied: "Everybody that is in the squad is going to be fit and available to start the game, so then it will be a decision whether it is too early or the right moment for him to make that step again."
Arsenal are also missing Riccardo Calafiori, Kieran Tierney and Takehiro Tomiyasu for the showdown with the Blues, while on-loan Chelsea attacker Raheem Sterling cannot face his parent club either.
Jorginho and Ethan Nwaneri are options to step into the engine room if Rice and Merino are both unavailable, while Gabriel Jesus could operate through the centre if Havertz does not make the cut.
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