"It is clear that I want to renew with Barcelona and I hope to be on the team next season", Umtiti said to L'Equipe.
Les Bleus beat Italy 3-1 on Friday evening, with Umtiti opening the scoring, and are still to play the United States before making their journey to Russian Federation.
His talents have not gone unnoticed, with United boss Jose Mourinho an apparent admirer as he looks to rebuild the Red Devils defence this summer.
Barcelona were concerned Umtiti's clause would be met amid reported interest from Manchester United, and therefore, according to ESPN FC, negotiated a £437m (€500m) release clause in the latest version of his agreement with the club.
Umtiti, 24, only joined Barca two years ago but his €60 million release clause left the club worrying that he could be tempted by the money on offer in the Premier League. Transfer speculation soon arose, and it seemed to have an impact on the centre-back, who regressed as the campaign wore on.
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"A great piece of news for the Barcelona fans, Samuel Umtiti will continue to wear the Cule shirt until 2023".
He is part of France's 23-man squad for the World Cup in Russian Federation and is expected to start alongside Real Madrid's Raphael Varane at centre-half.
Barcelona lifted the Copa del Rey during his first season, a feat they repeated in 2017-18 before also winning La Liga.
Umtiti will formally sign the five-year deal on Monday, before Barca hold a news conference.