The daily sports paper states that the Istanbul Giants are struggling to match the offers Inler has received from both the Premier League and Bundesliga.
Leicester City are currently in pole position to sign Inler according to the Sky Sports Italia reporter Gianluca di Marzio.
The report states that the Foxes have offered Inler €6 million plus bonuses on a three-year deal. Leicester want to bolster their options in midfield following the departure of Esteban Cambiasso earlier this summer and see the 31-year-old as a perfect replacement.
Fiorentina, West Ham, Hamburg and Werder Bremen are all also in the race to sign Inler according to Di Marzio.
Inler scored one goal in 33 appearances for Napoli in all competitions last season.
The Switzerland international has also previously played for Udinese, Zurich and FC Basel.