Arsenal manager Mikel Arteta sees Mohamed Elneny as part of his plans this season.
The Egyptian was the subject of interest from Turkish clubs Galatasaray and Besiktas.
Sky Sports says the Gunners rejected a bid from the former on Tuesday.
Arteta wants to use Elneny this season as he looks to push Arsenal up the Premier League table.
The Turkish giants have until the close of their domestic transfer window on Wednesday to conclude a deal for the 29-year-old.