The 34-year old veteran decided against renewing his contract with Leicester City after having a stellar debut season in the Premier League with the East Midlands club.
Cambiasso's father and agent, Carlos confirmed the news in an interview with SportsDNA: "It is true that there are advanced talks with Olympiacos for Esteban, but I cannot confirm that we have agreed.
"In football, of course, things can change from day to day or even from hour to hour. Cambiasso is a free player and there is interest from other teams, I can tell you about two teams from the Premier League and Turkey.
"We continue to talk with everyone, we have not closed. Our talks with Olympiacos are well advanced and I hope soon to have announcements.
"Esteban is definitely keen to come to Greece and Olympiacos. It is a team that will play in the Champions League and this keeps him right now at the highest level.
"I cannot tell you about money or contract duration, these are issues to be resolved."