The Chelsea boss has backed the pair to succeed at their respective clubs if they get the time to turn things around
Both sides have been struggling to find their best form in Serie A this season, but Mourinho feels the two Milan clubs simply lack the quality to compete at the moment.
"I believe that Mazzarri and Seedorf need time and support from their clubs and fans," Mourinho told La Gazzetta dello Sport.
"Let's be honest, they don't have a lot of top players to build a great team in just a few months, so they need some time and support.
"I am an Interista and will always be one. I think that Mazzarri deserves the club's faith.
"Of course, I am no Milanista, but I have a lot of respect for the club and their great history. I hope that Clarence will also get the chance to work in tranquillity and bring Milan back to the heights of before.
"Italian football needs the two Milan sides to be on top of their game."
Inter currently sit sixth in Serie A, while Milan have to settle for 10th spot at the moment.