The Gunners have made an unbeaten start to the season in all competitions ahead of Saturday’s trip to Bournemouth in the Premier League.
They defeated PSV Eindhoven in their opening Champions League game earlier this month and beat Brentford on Wednesday to reach the fourth round of the Carabao Cup.
Elneny came off the bench in that win at Brentford as he steps up his recovery following a serious knee injury in January.
And asked if thinks Arsenal have the depth in the squad to challenge for four trophies, he said: “Yeah. We can see how good the players were today and everyone performed really good.
“We had Reiss [Nelson] today score a goal and I think everyone, they are ready to play and we have enough numbers to play - because we play every three days a game and we need every player and everyone has to be ready.
“I think every moment is different and I think before we had good players as well and now it’s different. Different team, different players and a different manager as well.
“Mikel [Arteta], I’m happy for him because he’s done an amazing job with us and for this football club. I think because of this, we’ll be reaching the highest level.”
Elneny is currently the longest-serving player in the Arsenal squad, having been with the club since 2016.
The Egyptian signed a new contract earlier this year and Arteta has praised him for being “the glue” in the dressing room.
“I’m always positive around the lads and I try to make everyone together and make everyone to be positive in the dressing room,” he said.
“It’s good to have, not because of me, it’s good to have players to give good energy for everyone to be ready to train, to be ready to be around each other, to make the atmosphere really good between here and the dressing room. I think that’s everything we need.
“This is what I do every day. I come with a smile on my face, I do training, I help my teammates to train really hard - and on the pitch as well I try to give the best for the team.”