The 49-year-old Portuguese has been linked with a move away from the club at the end of the campaign after reports of dressing room unrest as well as board disagreements filtered through.
However, Callejon, who has been an impressive performer under Mourinho since returning to the club from Espanyol last summer, does not believe his manager is looking to quit the Spanish capital.
He told AS: "I don't think he is going to leave because he is happy here. He wants to work and do things right. I see him as calm and with the desire to win many titles."
Real Madrid currently hold a seven-point lead over Barcelona in La Liga and are through to the knockout stages of the Champions League.