The Burkina Faso international joined the French outfit in January 2008 and helped Didier Deschamps' side to the Ligue 1 title last term.
The 22-year-old has been linked with Sunderland, West Brom and Stoke City but wants to stay put for the challenges ahead.
He told Sky Sports' website: "I want to prolong my stay with Marseille, I love this club and want to do well here.
"We will have a great chance next season to win the league again and challenge for the Champions League, so I want to be part of that."
Meanwhile, Kabore is delighted for Marseille team-mate Andre Ayew after Ghana made it into the last eight of the World Cup.
He added: "They are making Africans very, very proud. My friend Ayew is doing fantastic, I am proud of him and the Ghana brothers. Come on Ghana!"