Former Real president Ramon Calderon recently claimed the club's Portuguese players are afforded special privileges by compatriot Mourinho and that their Spanish team-mates are resentful of them.
There were also reports last week that Casillas and Sergio Ramos had a changing room bust-up with their manager after the Copa del Rey loss at home to Barcelona.
However, Spain's World Cup-winning captain says that all is harmonious at the Bernabeu, labelling claims to the contrary "absurd".
"I don't have a bad relationship with any team-mate," Casillas told the club's official website. "We coexist in training sessions, pre-match gatherings and games, like all other squads.
"I may get angry with someone one particular day, or someone may get angry at me, but it's not something to dwell on.
"There are no problems between the Spaniards and Portuguese on the squad. I find it quite absurd also because there happens to be Brazilian players amongst the so-called Portuguese group."
Meanwhile, Mourinho insists he is unfazed by some of his own fans whistling and booing him in Sunday's win against Athletic Bilbao.
"I'm not bothered by the whistles at me,'' he said. "It's not a problem. It's the first time it's ever happened to me. There's a first time for practically everything. (Zinedine) Zidane was whistled at here. Ronaldo has been whistled at here. Cristiano (Ronaldo), who is the latest Golden Boot winner, has also been whistled at. Why can't I?
"Zidane responded with his football, the same as Ronaldo and Cristiano. I work hard to be able to respond like they did some day, but there may come a day when the fans are sad.
"There have been no problems this week. I lost a match on Wednesday (Copa del Rey first leg against Barcelona), but I was already thinking about tonight's game on Friday. We played and won. That's it.''
Real Madrid are currently five points clear of Barcelona at the top of La Liga as they chase a first Primera Division title since 2008.