Barca see Kane as an alternative to Borussia Dortmund ace Erling Haaland.
But Haaland's club will seek a fee topping £150million if they are to sell him this summer, with the 20-year-old's £68m release clause activating next year.
That could turn Barcelona to a Plan B, reports Sport, who name Kane and Lautaro Martinez as such options.
But Tottenham will refuse to sell their star striker to a Premier League rival.
A move abroad is considered slightly more palatable, although the fee of £175m would have to be negotiated down.