Gunners manager Unai Emery has instructed the out-of-favor pair to pursue "another challenge" after he made it clear they don't feature in his plans this season. Mustafi and Elneny can move to a club on the continent before the European transfer window closes Sept. 2.
"They are very big players but for one circumstance or another they are going to have fewer chances to show their capacity or to be happy with us and the minutes they play in matches," Emery said, as reported by the Guardian's Nick Ames.
"Last year with Mustafi and Mo, when they didn't play they weren't happy and I spoke with them a lot of times last year and this preseason. I think it is positive for them to leave and sign for another team where they can be protagonists and be happy and continue their careers."
Mustafi's availability has alerted AS Monaco and Elneny is interesting outfits in Turkey, Ames reports.
Mustafi, 27, moved to Arsenal from Valencia for around £35 million in the summer of 2016 and has since appeared 84 times in the Premier League. The German international started 31 top-flight matches last term but was often scapegoated for errors in the Gunners' oft-haphazard backline.
Elneny arrived seven months before Mustafi and has played in 38 fewer Premier League matches. Granit Xhaka, Lucas Torreira, Matteo Guendouzi, and Ainsley Maitland-Niles were already challenging the Egyptian for minutes in central midfield before Elneny slumped further down the pecking order this summer following the arrival of Dani Ceballos.