Ronaldo's future with the European champions has been under scrutiny since Spanish prosecuters filed a complaint in June alleging he evaded €14.7million in taxes relating to image rights from 2011 to 2014.
Reports this week also suggest the 32-year-old wants a new contract at Madrid that will be more lucrative than Lionel Messi and Neymar's respective deals at Barcelona and Paris Saint-Germain.
Asked about the speculation surrounding Ronaldo's future, Zidane said "I don't talk about money here. This is an issue for Cristiano and the club, not for me.
"No, not at all [whether he fears Ronaldo's departure]. There has been a lot of talk but no substance. Cristiano is here and he's not going to leave.
"This is his club, his city, his team and I think he's very happy to be here and with everything he's got here.