The 28-year-old scored two goals on Wednesday night as los Blancos beat Chelsea 3-1 in the final of the Guinness International Champions Cup and celebrated by pointing his finger at the club's crest.
However, the Portugal international has been linked with a return to Manchester United, while the club have continued to pursue Tottenham winger Gareth Bale.
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“We are all convinced that he will end his playing days at Real Madrid,” Perez told ESPN.
“At the end of the summer we will try to resolve this matter.
“The season starts next week, but before the end of the month or the beginning of next month, I'm sure [it will be sorted out].”
“There is no great hurry because there is good will on his part and we will resolve it satisfactorily. At least that is my wish, and I believe it is his too.”
Earlier this week, the former Man United star was named on a three-man shortlist, along with Lionel Messi and Franck Ribery, for Uefa's Best Player in Europe award.
Ronaldo is entering his fifth season with the club and has scored 146 goals in 135 games since arriving at Santiago Bernabeu.