President Florentino Perez believes the 50-year-old has the personality and character required to take over at the Bernabeu
resignation of Zinedine Zidane.
And they have identified Klopp as the leading candidate to take over the biggest job in football at the Bernabeu.
But Liverpool will fight tooth and nail to keep the charismatic German who still has another four years left on his Anfield contract.
Spurs boss Mauricio Pochettino, long admired by Perez, is also on the radar and that option will be explored.
But Klopp, 50, has shot to the top of the Madrid wish list after guiding the Merseysiders to Saturday’s Champions League final in Kiev, where they lost 3-1 to the Spanish giants.
President Florentino Perez believes Klopp has the personality and the strong character required to handle the demands of the world’s biggest club.
And he hopes that the once in a lifetime opportunity to manage the 13-time European Champions will prove irresistible for the former Dortmund boss who took charge at Liverpool in October 2015.
There is no buyout clause in Poch’s contract, nor was there one in his previous deal, and there’s no gentleman’s agreement that he could talk to Real if there was an approach.
Tottenham are under no illusions that their highly-rated boss is likely to manage Real at some point in the future.
But Spurs chairman Daniel Levy fully expects Pochettino to remain with the North Londoners this time around.
Klopp currently earns £140,000-a-week on Merseyside but Real are ready to offer him a deal worth £10million-a-year.
And they are also working on a £100million move for superstar striker Robert Lewandowski, who played for Klopp at Dortmund and has now told Bayern Munichthat he wants to leave.
Liverpool’s exhilarating brand of attacking football has convinced Perez that Klopp is the right man to knock bitter rivals Barcelona off their perch at the top of La Liga.
The Spanish giants have made three unsuccessful attempts to appoint Arsene Wenger in the past but have gone cold on the former Arsenal manager in recent years.
Wenger, 68, is now finally open to offers after leaving the Emirates last month and would jump at the chance of taking charge at the Bernabeu.
He admitted this week: “Real Madrid is one of the teams I loved when I was a kid and I want to be tested again in my life.
“I am a competitor and I want to get back to what I have been good at.”
But the Frenchman’s age combined with his failure to win a single European trophy has convinced Perez that the Frenchman’s best years are behind him.
Prising Klopp out of his Liverpool commitments would cost £28million in compensation payment.
And the German has expressed no desire to leave Anfield despite failing to win a trophy during his time in England.
A far cheaper alternative would be former Bernabeu legend Guti, who is currently the club's youth coach.
And among other names in the frame are Juventus boss Max Allegri and Chelsea’s Antonio Conte.
Yesterday’s surprise announcement means that Gareth Bale is now almost certain to stay at Madrid.
The £85million Welsh superstar was furious at being left out of the starting line-up for Saturday’s Champions League final and was considering his future at the club.
But Zidane’s departure has changed Bale’s thinking and a Premier League return is now increasingly unlikely.