Sport says Barca are in contact with Kane's camp and have registered their interest.
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The Blaugrana see Kane as a replacement for Robert Lewandowski, who is off contract at the end of the season.
Kane, with a deal to 2027, can leave Bayern next year for a set fee of €65m - and Barca are keen.
For their part, Bayern are ready to open talks with Kane about a new contract extension.
Other centre-forward targets being considered by Barca are Erling Haaland (25/Manchester City), Julián Álvarez (25/Atlético Madrid), Karl Etta Eyong (21/UD Levante) and Dusan Vlahovic (25/Juventus).