The 29-year-old is currently Arsenal's longest serving player but his contract expires at the end of this season.
Elneny joined Arsenal from FC Basel in January 2016 but he has not always been a regular at the club.
After spending the 2019/2020 season on loan at Besiktas, Elneny returned to Arsenal last season and made 41 appearances across all competitions.
Opportunities have been scarce this term, with the Egypt international making just nine Premier League appearances and 12 in all competitions.
Elneny has started Arsenal's last two matches against Chelsea and Manchester United in the absence of Thomas Partey and has impressed in victories in both big games.
Having gained the trust of Mikel Arteta, Elneny is prepared to extend his stay at the Emirates Stadium.
“If Arsenal say: ‘We want you’, I don’t think about leaving,” the Egyptian said after the Gunners' 3-1 win over Manchester United on Saturday. “It’s my family for six years. I love this club.
“I always love a challenge and give 100 per cent all the time. I don’t decide who plays, but I keep going in training to show how good I am and to make him (Arteta) play me. If I don’t play I keep going until I get my chance. The contract and stuff, I’m just waiting for the club to decide what they want.”
“I’m really happy to be one of the starting XI for these two games," Elneny said. "I gave everything in training to be one of the starting XI every game and I got my chance and I think I did well. Most importantly, we won the two games.
“It’s been a long wait for me but you have to believe. I have to train hard every day, focus all the time to wait for a chance and when it comes you have to give everything just to keep it.
“He (Arteta) just trusts me and he put me in the big games, and I have to thank him for that. I will keep going and not think about anything else, just focus on my performances to help the team reach our goal."
