The Egypt international has spent the past campaign on-loan with Besiktas.
The Gunners are willing to sell, though a return to Besiktas is a remote possibility at this time.
Instead, Newton hopes to sign Elneny for a new 12-month loan at Trabzonspor.
Newton is already in talks with Elneny about accepting a loan deal - which will cost Trabzonspor €1.5m.
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