The daily newspaper claims that the Foxes will make an initial bid of €7 million but are willing to pay up to €10 million for the 31-year-old.
Galatasaray are unlikely to be keen on selling their skipper however, due to their precarious financial situation they may let their star man leave at the right price.
Inan currently makes over €3 million per-season and has four-years left on his current deal at Galatasaray.
Leicester are targeting Inan as a replacement for Esteban Cambiasso who departed fromthe club at the end of last season,.
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.