The report states that the Foxes are looking for an experienced player to fill the role of Esteban Cambiasso who departed this month.
However, the 30-year-old has four years remaining on his contract with Galatasaray who have no intention of selling their star name.
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.
Selcuk provided 11 assists and scored seven goals in 44 appearances for Galatasaray last season. The Turkish international struggled under former manager Cesare Prandelli but entered a new lease of life following the appointment of Hamzaoğlu.