Los Blancos have drawn a blank in front of goal across their last four games in all competitions.
The side’s attacking lethargy has left them fourth in La Liga and second in their Champions League group.
Pressure is now building on Julen Lopetegui as the new boss tries to fix Real’s attack in the post-Cristiano Ronaldo era.
Gareth Bale and Karim Benzema began the season well and have both notched four goals in all competitions, but the recent torrid performances have worried president Florentino Perez.
And a report in Spanish newspaper El Confidencial has now claimed that the Bernabeu club are interested in signing Kane.
The 25-year-old Spurs striker was linked with a move to Madrid in the summer, but no official bids were lodged.
Instead, Kane signed a new £200,000-a-week contract with the Lilywhites, which ties him to the club until 2024.
Tottenham have maintained before that they have no intentions of letting their talisman leave the club.
It is thought that £200million would be a difficult price to turn down, but Real are reluctant to spend such a hefty amount.
The report claims that RB Leipzig striker Timo Werner is being eyed as an alternative.
The 22-year-old German striker has scored 34 goals for the Bundesliga outfit in the previous two seasons, and is seen as a thriftier option.
Meanwhile, Eden Hazard has reiterated his desire to join Los Blancos, though also said he is open to negotiating a new Chelsea contract, with his current Blues deal expiring at the end of the 2019/20 season.
If the Belgian forward does the latter, it will mean Madrid will likely have to fork out a nine-figure sum to gain his services.
Speaking after Chelsea’s 3-0 win over Southampton, Hazard said: “Real Madrid is the best club in the world. I don’t want to lie today.
“It is my dream since I was a kid. I was dreaming about this club. We will see. I don’t want to talk about this every day.”