Callejon, 25, is not one of Madrid's most famous names but made 36 appearances last season - the majority from the bench - and hopes to be given another chance to impress.
“I will not move,” Callejon told AS. “I am very comfortable in Madrid. I know Mourinho well, and he trusts me. There are many reasons why I want to continue.
“I will continue to demonstrate my commitment to Madrid, and help to win as much as possible.”
Callejon emerged from the youth ranks at the Bernabeu but started his top-flight career with Espanyol before returning to Madrid last summer.