A double from Cristiano Ronaldo, along with goals from Kaka, Angel Di Maria and Jose Maria Callejon helped Real to a 5-2 second-leg win.
Gustavo Manduca and an Esteban Solari penalty gave the Cypriots some consolation late in the match.
Mourinho said: “Bayern is a very powerful opponent. It is a team I know well as it is almost the same side that I played when coach of Inter Milan in the Champions League final two years ago and they have great individual players.
“The players and myself are looking forward to what should be a great semi-final.”
Jose writes off Chelsea
MAdrid: Real Madrid manager Jose Mourinho has written off former club Chelsea’s hopes of reaching the Champions League final, branding their semi-final opponents Barcelona as “super-favourites” to progress.
Asked why he had told Telemadrid that Barca would advance, he said: “Because they are very good. Barca aren’t the favourites, they are super-favourites. Let me be honest, I just don’t think it will be Real Madrid v Chelsea and we know why.”