The two men had a poor relationship towards the end of Mourinho's reign at the the club last season, with Casillas being dropped to the bench for much of the season. Despite this, the 32-year-old says he will be courteous towards his former boss should he see him.
On his past feud with the 50-year-old coach Casillas added: "It's just another experience in the world of football. You have to focus on the future and leave behind the past. I've come out unwounded. There were positive things from Mourinho's time in charge and they must be cherished."
The Spain international also spoke about his Madrid team-mate Cristiano Ronaldo, who he believes is the best footballer on the planet at the moment.
"There is no arguing with Cristiano Ronaldo's record and statistics," he said.
"He's been at Real for four years and has performed to the best of his abilities. In my opinion, he's the best player in the world. There will always be different criteria, but he is now the best."
Finally, Casillas gave his thoughts on potential Madrid signing Gareth Bale, as well as the threat Barcelona pose this season.
"Real Madrid will try to bring the best players to the club. The squad is currently very well balanced but a player like Bale will always be welcome."
"Messi and Neymar are both good players, along with [Andres] Iniesta, Xavi and others. But Real Madrid has been on a par with Barça for a few years now."