The Egypt international is believed to want regular first team minutes and that looks unlikely to come anytime soon, with Granit Xhaka and Lucas Torreira firmly established as the club's first choice central midfielders.
According to the Mirror, the midfielder will see what options are available to him in the January window, with Leicester reportedly interested in bringing the former Basel man to the East Midlands.
However, while there are no further details in the report, the Evening Standard have reported that Elneny has been told to leave the club on loan, having made just seven appearances under Emery.
Leicester have options in central midfield, with Wilfred Ndidi particularly impressive alongside Nampalys Mendy, while Hamza Choudhury has had a decent run in the side, featuring in the wins against Chelsea and Manchester City.
Elneny has also been urged by Hamdy Nouh, the coach of Egyptian side El Mokawloon, to leave Arsenal and try to regain some confidence.
"He has been influenced lately by the change in coach and his new style, but I am confident that he will return better than before, because of his great potential and the competitive spirit that will help him get back in."