The Portuguese tactician took the reins at the Santiago Bernabeu in 2010 before ending a three-year trophy drought in his first season in the form of the Copa del Rey.
He then went on to win the Spanish club's first La Liga title in four years in 2012 and feels United's current predicament is very much the same as what he experienced in Madrid.
"I would say it's similar to the Real Madrid one because they were two giants in two difficult periods," Mourinho told Sky Sports.
"You go to the giant club, you feel the dimension, you feel the pressure and you feel the expectation.
"But you also feel the club is not ready, not ready for this kind of expectation and you have to work more.
"And then you have to fight more. So I would compare my arrival here to my arrival at Real Madrid.