The LaLiga giants are looking to land a world-class striker ahead of next season and believe Kane is the perfect man to sign.
Real are also interested in Paris Saint-Germain forward Kylian Mbappe and Borussia Dortmund striker Erling Haaland, but believe Kane is more attainable.
Los Blancos feel negotiations with the English striker would be “easier” than with either Mbappe or Haaland.
Kane’s older sibling, Charlie, is registered as an intermediary to manage his football and commercial affairs and Real believe “other intermediaries could make the operation considerably more expensive”.
Mbappe appears to be represented by his relatives, while Haaland is a client of super agent Mino Raiola.
Kane has scored 215 goals in 377 games over eight seasons for Spurs, but has failed to win any trophy.