The 30-year-old has been strongly linked with a move back to his old club AC Milan throughout this summer.
"I think Kaka is in a better position than me to talk about his future," said Mourinho on Saturday. "He knows better than me what he is thinking and what his intentions are.
"As coach of Real Madrid, I limit myself to getting the best possible performance from my players, and if in the end on September 1, he is here and he plays for us in the 2012-13 season, then I'll respect him and try to get the best possible performance from him.
"This is what we did last year and we managed to get him to achieve things which turned out to be important."
Kaka joined Madrid from Milan in the summer of 2009 and won La Liga with Los Blancos last season.