The Portuguese will leave the Spanish capital at the end of the season after a controversial three-year reign, which saw him reportedly fall out with a host of players.
"Mourinho's last game is on Saturday and I hope he has success wherever he goes," the former Valencia man told AS. "It will always be necessary to keep the things that I have learned from him and I for my part do not have any problem with him.
"Each coach has their preferences and tastes but they must be respected. I wish him well."
Albiol has been used sparingly during his time at the Bernabeu but insists that he is not looking to leave the club.
"I am very happy at Real Madrid," the 27-year-old continued. "I have a contract here, I am grateful to everyone and like any player, I want to be at Real Madrid. Now there will be many movements of coaches but you have to wait to see what happens.
"I am a person who likes to keep things positive and I'll take what I've learned in the past three years with Mourinho. I've gone through good times and bad times. This season has not been easy. We haven't won any titles and we're all disappointed. We always want to win titles."
Real Madrid wraps up its season, and Mourinho's reign at the club, by hosting Osasuna on Saturday.