Cambiasso released a statement confirming that he will not renew his current deal with the Premier League club.
The statement read: “I have decided not to renew my contract with Leicester City.
“I have taken this decision only 24 hours after receiving the proposal from Leicester because I want to give the club as much time as possible to find an alternative.”
Besiktas are on the look-out for a new central-midfielder following injury to Tolgay Arslan. The former HSV midfielder has been ruled out for at least six months after tearing a knee ligament during pre-season training.
The Argentina international was Leicester’s player of the season and previously worked with the newly appointed Claudio Ranieri at Inter Milan.
The 34-year-old joined Leicester City on a free transfer from Inter Milan last summer. Cambiasso has previously played for Real Madrid, Ricer plate and Independiente.
Cambiasso scored one goal and provided five assists in 33 appearances for Leicester last season.