The Spain captain believes the Portuguese coach made an important contribution to Real Madrid during his three-year spell and believes Gareth Bale is one of Europe's very best
Mourinho won three trophies during his three-year stint at Santiago Bernabeu, although the latter part of his tenure is best remembered for a public fallout with Casillas which led to the club captain being frozen out of the first team.
Casillas, however, has stressed that the current Chelsea boss' efforts in La Liga cannot be ignored, although he is relishing the prospect of beginning a new campaign under replacement coach Carlo Ancelotti.
"I've only been training with Carlo, I don't know what differences there are [between Ancelotti and Mourinho], but it's not a question of looking back. You have to be grateful for Mourinho's contribution to Real Madrid, but now we have to start with the hope that the club can be at the top," he told a press conference.
"He's a winner, that's obvious to everyone, but he'll make it clear from the beginning. This club was on the edge of titles last season; we want to complete our objectives in all three competitions."
Madrid have been heavily linked with a renewed push for Tottenham star Gareth Bale in the coming weeks, with Spurs determined to hold on to their star man despite his desire to leave, and Casillas is not surprised to see los Blancos once again chasing one of Europe's finest.
"We're talking about a player who, frankly, is one of the best three or four players in Europe, and it's normal to talk about him," the 32-year-old said. "We're talking about a decisive player. The market is still open and I'm sure someone will arrive here before the beginning of the Liga season."
Finally, Casillas says competition for places at the club is good under Ancelotti - but admitted he was desperate to regain his No.1 spot next season.
"Competition is always healthy. There are very good goalkeepers here and we must learn to live with that. I hear a lot about competition for my post, but in other parts of the pitch there are two or three players for one position as well," he added.
"I would love to be No.1 keeper. I work for it. But if you ask the others, they're going to say the same. You have to compete to play in the XI of Ancelotti. I will have to fight as I always have."