El Pais says Perez was pondering dismissing Mourinho during the winter break after the Special One blew up following their clash with Sevilla.
At the club's Christmas function, Perez declared: "There are people who act like this is just any normal club and do not realise that Real is the biggest. The pressure that is experienced here is not for everyone, some turn loco."
The comments cut no ice with Mourinho, who at the time replied: "President, I am the coach you expected and you are the president I expected."
The clash came after the 5-0 result at Barcelona, Mourinho's row with Jorge Valdano and his demands that Pepe be re-signed.
Florentino had great concerns with the way the season was going, but in the end chose to back the coach - and was rewarded with last week's Copa success and the run to the Champions League semifinals - and possibly further.