The Egypt international is not a first-team regular at the Emirates Stadium but, with Arteta operating with a small squad, his absence could be felt in the Premier League title race – especially with FA Cup and Europa League fixtures in the mix.
Arsenal have already signed Belgium forward Leandro Trossard from Brighton and Jakub Kiwior – a highly-rated Poland international defender – in the January window.
The Gunners sit five points clear at the top of the Premier League and travel to face closest challengers Manchester City in the FA Cup fourth round on Friday night.
Arteta revealed Elneny will not feature due to a knee injury suffered in training, with a return date for the 30-year-old not forthcoming.
The north London club have been linked with a summer move for West Ham captain Declan Rice but may have to strengthen in the current window.
“There are concerns,” Arteta replied when asked about suggestions Elneny could be out for the season.
“Mo is a player who never complains about anything. But let’s see. He had some issues with his knee that we are assessing at the moment.”
Pushed on whether it could mean Arsenal return to the market – with the likes of Amadou Onana, Weston McKennie and Moises Caicedo linked – the Spaniard added: “Well, we need some more cover in midfield ideally if we can.
“In this market it’s pretty complicated to do that. The most important thing is that we get the performances and the time on the pitch that we need with the players we have available today that are already really good.
“If there’s anything else available that can make us better, we’ll look at it.”
As well as Elneny, Gabriel Jesus is also on the sidelines with a knee injury and will miss the game against his former side City.
“With him, I don’t know,” added Arteta. “He wants to be here next week but it’s unrealistic. He’s pushing and driving everyone to the limit.
“I can’t give you an answer. Hopefully it will be weeks and not months, but it was a serious injury and we need to respect that process as well.”
The game at the Etihad Stadium will see Arteta come up against close friend Pep Guardiola, who he also worked under at City.
Asked if his relationship with Guardiola had changed now the two are going head to head for the title, Arteta replied: “I always hoped that that was going to be the case one day and it’s happening this season.
“That’s not going to change any friendship, the moments that we have, how important he is in my life, how important he is in my profession.
“We’re both willing to win and defend our clubs in any way and that’s always been the case since day one.
“I would prefer to do it with someone else to be fair. I want the best for him, genuinely, and when you are challenging with someone like this something comes in between that.
“So it’s a strange feeling, it is what it is, and that’s our challenge.”