Klopp seems relaxed at Liverpool and has a good rapport with many members of the first-team squad.
It has been that way ever since he succeeded Brendan Rodgers in 2015, with Mamadou Sakho his only high-profile row.
Real Madrid players tend not too react too well to managers who like to impose themselves.
Jose Mourinho infamously lost the dressing room when he was in charge, clashing with Sergio Ramos, Iker Casillas and Ronaldo himself.
It was a similar story for Rafa Benitez, whose head rolled with players struggling to buy into his methods.
Real Madrid star Cristiano Ronaldo fears Jurgen Klopp would be too strict (Image: GETTY)
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Klopp sings with Liverpool fans after Champions League final
And Diario Gol say Ronaldo has similar fears regarding Klopp.
The Liverpool boss is not, however, thought to be among the frontrunners for the managers job.
Tottenham’s Mauricio Pochettino was earmarked as an early favourite.
And, since then, Guti, Max Allegri and Antonio Conte have all been tipped to take over.