The Romania international joined Inter from Roma for a reported fee of 16 million euros in 2007 and helped them to win league titles in 2008, 2009 and 2010 and the Champions League in 2010.
"My future? At Inter!" the 32-year-old, capped 75 times by the Balkan country, was quoted as saying in Romanian media on Tuesday. "At least I hope so, if they don't get rid of me!
"I'm joking, I'm happy, really happy here and the club is happy with me," added Chivu, who can play as a central defender, left-back and defensive midfielder. "I'll finish my career here."
Chivu, who has not played since Inter's 3-0 win at Hajduk Split in the Europa League on August 2 when he suffered a toe injury, is expected to return to action when his team host Verona in a Coppa Italia last-16 match on Tuesday.
"I feel good, the last four months were tough but I'm better now," Chivu said. "There were complications which meant I needed a second operation but now I feel fit enough to help out."