The Frenchman manager has been poor with the Madrid team this season and could just be on his way out this season should his squad fails to defend the Champions League this season as the only competitions they are still involved in.
According to report from the Sun, the Reds boss is the prime target for the Los Blancos due his style of attacking.
The German coach has been renowned for his work in the Liverpool team since his appointment three years ago, might just not be leaving the club this season despite the interest from the Los Blancos.
Klopp has used his attacking tactics to lead the Reds team to the Champions League finals after defeating Premier League leaders Manchester City in the quarter-finals 5-1 on aggregate and could just be up for the second position in the league with Manchester United currently retaining that position.
However, Real Madrid are not only interested in the signing of Klopp, but also their summer signing Mohamed Salah, who has been impressive in his run of form for the Reds this campaign as he has bagged 39 goals in all competitions so far.
Mo Salah has also been tagged to become the top scorer in the English Top Flight this season as he is currently leading with 29 goals, and 4 goals ahead of former top scorer, Harry Kane.
Real Madrid will really have some convincing to do should they become desperate to sign the Liverpool duo in the summer, as Klopp is not interested in leaving Anfield this season.