The 32-year-old has voiced his opinion that there is no time to think about the club's recent successes as they are re-building the team
The former Romania international is one of the remaining players from the team that won a historic treble with the Giuseppe Meazza in 2009-10, but he feels the time has come to move on from past successes.
"If we talk about past achievements we’ll never achieve our goals for the future," Chivu said at a press conference.
"Our past victories are part of those stories that you tell your grandchildren, that will stay in the fans' hearts. But now our current goals are what matter. Enough with the past.
"We’ve said thanks where it’s been necessary, but now is not the time to have memories on our minds.
"This Inter side is growing. We have a new coach and many youngsters, some of whom are still in their teens. We’ll put the past behind us."
Inter's last major title win was the Coppa Italia in 2011.