The 28-year-old is the second top goalscorer in Tottenham's history with 221, but is yet to win a major trophy at club or international level.
Kane had made clear his desire to leave his boyhood club in the quest to end his wait for silverware.
However, he still has three years left on a six-year deal signed in 2018, allowing Spurs chairman Daniel Levy to demand a fee well in excess of the £100 million English record City paid Aston Villa for Jack Grealish earlier this month.
He posted on Twitter. "I will be staying at Tottenham this summer and will be 100% focused on helping the team achieve success."