Elneny is on-loan this season at Besiktas from the Gunners.
Ljungberg has said he is working game by game but, if Arsenal cannot find a long-term manager, Elneny believes the former Sweden international can take charge for the rest of the season.
"Yeah, 100 per cent," said the 27-year-old, who joined from Basel in 2016.
"I worked with Freddie before I left and he's a really good coach. Why can't he continue if Arsenal don't find the new coach."
Of his own future, Elneny stated: "I'm 100 per cent focused on Besiktas now, I want to win the league and the cup.
"It feels like it's my home now, I'm happy here, we play good football with a really good coach.
"The team will become stronger every game and I have a really good chance to be successful with this team."