That is according to ESPN FC pundit and former Chelsea midfielder Craig Burley.
Real Madrid crashed out of the Champions League at the last-16 stage on Tuesday night and are 12 points behind La Liga leaders Barcelona.
Tottenham striker Kane has been linked with Real in the past and has had another fine season in England.
He has scored 16 Premier League goals despite missing four matches due to an ankle ligament injury earlier this year.
Burley believes Real must go all out to sign the England captain and get rid of Gareth Bale and Karim Benzema in the process.
“There’s only one way out of this for Real Madrid and that’s spend, spend spend,” Burley said.
“Harry Kane, that’s the kind of player they’re going to start going after.
“Getting rid of the Benzemas, getting rid of the Bales, getting rid of all these guys that are deemed not good enough for this team anymore.
“And they’re going to have to go to Europe and the rest of the world, South America and spend big on players like Harry Kane and other positions to get themselves back up.”
Bale’s future at the Bernabeu is in serious doubt following explosive comments from his agent Jonathan Barnett earlier this week.
Barnett is not happy with the treatment of Bale from some sections of the Real support
“This generation of Real fans will be talking about Gareth’s goals for years to come,” Barnett said.
“Frankly they should be ashamed of themselves.
“Gareth deserves the greatest of respect. The way the Real fans have treated Gareth is nothing short of a disgrace.
“In the six years he has been in Spain, he has won everything.
“He’s one of the best players in the world.
“Those fans should be kissing his feet.”
Bale came on as a first-half substitute in the shock Champions League defeat to Ajax on Tuesday.
