The Tottenham striker is much sought after, having netted more goals than any other player in 2017.
Kane found the back of the net on 56 occasions – twice more than Barcelona’s Lionel Messi.
And Real Madrid are currently on the lookout for a new striker this window to try and save their season.
Karim Benzema is currently misfiring with only five goals to his name this campaign, so president Florentino Perez is desperate to secure the signature of Kane.
According to Spanish outlet Don Balon, German sports company Adidas are playing a big part in helping the move pull through.
Real Madrid’s current sponsorship with Adidas is due to expire in 2020 and both parties could soon agree an extension.
Kane is one of the main faces of the Adidas brand and helping him move to the Spanish capital would suit both parties, according to the report.
It is suggested that Perez is very keen on the idea.
However, Spurs have not yet received an approach for their top goalscorer and they would not consider selling him should Real make their move.
Manager Mauricio Pochettino is keen to keep the sharp shooter at Wembley.
But if Real table a former offer it may be too good for the England international to turn down.