Kane is now heading into the final year of his contract at Tottenham and is a wanted man as the summer window looms.
Manchester United have been strongly linked with Kane, who also has other admirers in the Premier League.
Spurs are firmly opposed to selling Kane, who they value at around £100m, to another Premier League club, leaving Real Madrid as the most likely option if he does move.
There are question marks over whether Real Madrid would agree to pay £100m for Kane, but they may be able to get him for less.
It is suggested that Levy could be tempted to do business if Real Madrid offered £80m and achievable add-ons later in the transfer window.
Having lost Karim Benzema, Real Madrid view Kane as their top target to slot in and replace the Frenchman.
Incoming Spurs boss Ange Postecoglou is likely to want to keep hold of Kane and is expected to hold talks with the striker.