The England captain's current deal expires next summer, and Bayern are keen for Kane to stay, as per the BBC.
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The 32-year-old is aware that Bayern want him to stay, and will continue talks with the club in the coming weeks.
Kane joined Bayern from Spurs in 2023 in a reported £86 million deal, and has lifted two Bundesliga titles and the German Cup.
The striker has attracted interest from several top clubs around Europe, including Barcelona who have had a long-standing interest in Kane.
He has also attracted interest from clubs in Saudi Arabia, but for now, Kane wants to stay in Europe and compete for titles.
