The Daily Star report that the Premier League outfit want to replace Estian Cambiasso with the Galatasaray captain.
Inan currently makes over €3 million per-season and has four-years left on his current deal.
Cambiasso recently confirmed that he will leave Leicester according to the BBC. The former Argentinian international released a statement saying that he will not renew his current deal with the Foxes.
The statement read: “I have decided not to renew my contract with Leicester City.
Cambiasso scored one goal and provided five assists in 33 appearances for Leicester last season. The 34-year-old joined Leicester City on a free transfer from Inter Milan last summer.
Inan provided 11 assists and scored seven goals in 44 appearances for the Lions last season.
The 30-year-old midfielder is a regular Turkish international and has won three Super Lig titles over the past four season. Inan played a key role in Galatasaray winning the league title for an unprecedented 20th time last season.