The midfielder fell out of favour under former Arsenal boss Unai Emery and was loaned out to Turkey in the summer of 2019.
Elneny impressed at Besiktas, though, and was given a second chance by Mikel Arteta when he returned for pre-season training last summer.
“I expected to come back because I want to always be with the biggest team and I am really happy to be at Arsenal all the time,” said Elneny.
“When I was on loan, all the time I was thinking I need to get back to Arsenal to be in the squad, to play like I do now.
“That’s why I worked really hard in Besiktas and I built myself there to come back stronger.
“Before I came back, Mikel didn’t speak to me, but after when we came to the start of the season he started to speak to me.
“And he said: ‘Mo, we have new things now. We have to understand how I want the midfield to play and always if you don’t understand something from the new system you have now, just come to ask me’.
“He was helping me so much to understand the way he wanted us to play and this is what helped me a lot.
“After the Community Shield against Liverpool, he came and sat down with me and he just gave me everything I’ve done, with the pre-season and the game against Liverpool.
“And it was something really good for me to start the season with.”
Elneny will have one year left to run on his current contract in the summer and says he would love to sign a new deal with Arsenal.
“Of course, for me I am always loyal to Arsenal,” he said. “And if Arsenal say to me: ‘Sign a new contract’, of course I would be happy to do this.”