The France international was linked with a move to Manchester United over the summer after losing his place at Barca while out with injury last season.
Umtiti, who played a key role in France’s 2018 World Cup triumph, has continued to struggle for fitness and starting opportunities this season under Ernesto Valverde.
The 26-year-old has made just four appearances in all competitions so far, although he has started Barcelona’s last three games alongside Gerard Pique.
“You never know, it could happen, I don't know. I'd love it, I'd love to end my career here at Barca but I'm young, right," Umtiti told Sport at a Puma event.
"I have time and I have to play, play, play and win titles."
The centre-back joined Barca from Lyon for €25 million in the summer of 2016.
Umtiti played in all but one of France’s games during their World Cup triumph in Russia, scoring the winning goal in a 1-0 semi-final victory over Belgium.
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