Ronaldo, 32, is said to want to leave Spain after being accused of tax fraud.
The forward, with the Portugal squad in Russia, signed a new five-year contract in November 2016, but has been linked with a return to Manchester United.
"The only thing I can say is Cristiano Ronaldo is a Real Madrid player," said Perez, who was re-elected on Monday.
Spanish prosecutors have accused Ronaldo of defrauding the authorities of millions of euros in tax, which he has denied.
"Obviously something has happened, something has affected him, his credibility," Perez told Spanish radio station Onda Cero. "I'm sure he will tell us and we will see.
"It's no coincidence that he's in a very important tournament, the Confederations Cup. It hasn't finished yet and I don't want to disturb the Portuguese team.
"He just wants to be the best player in the world. If Cristiano wants to leave Real Madrid, it won't be for money."
Perez said he is yet to receive an offer for Ronaldo - or striker Alvaro Morata or midfielder James Rodriguez, both of whom have also been linked with United.
"We want to keep all our players next season, including James," said Perez.
Speaking in a further interview with Spanish newspaper Marca, he added: "Cristiano is a good guy as a professional and as a person. This is very strange and in the next few days I'll talk to him.
"I must defend him at all costs, both as a player and as a person. What I will say is that everyone must fulfil their tax obligations. I have no doubt that Cristiano will be able to defend himself.
"What they have told me is that he has the same financial arrangements as he had in England, where he had no problems."
Ronaldo is said to be "upset" after being accused of tax fraud and wants to leave, a source close to the player told the BBC.
He is accused of evading tax to the value of 14.7m euros (£13m; $16m) between 2011 and 2014.
Real Madrid released a statement saying they had "full confidence" in their player, and they were convinced he would prove his innocence.
Ronaldo's discontent has alerted clubs all over the world but he has been linked most strongly with a return to United, or a transfer to PSG.
But the Portuguese would be costly - his Real contract has a 1bn euro (£874.88m) release clause.
In 2009, Perez - then in his second spell at the club - signed Ronaldo for Real for a then world-record fee of £80m.
The forward had helped United win three Premier League titles and the Champions League in his six years at the club, and had also won the Ballon d'Or.
He was presented at the Bernabeu in front of 80,000 fans, as Perez attempted to bring together a second group of 'Galacticos'.
Eight years on, Ronaldo has scored a club-record 406 goals in 394 appearances.
Only two weeks ago, he helped Real win their 12th European Cup, scoring twice in a 4-1 victory over Juventus in the Champions League final in Cardiff.
Victory meant Real became the first team to win back-to-back Champions League titles, with Ronaldo the competition's record goalscorer with 105.
A two-time La Liga winner, his 285 goals in 265 league appearances mean he is second only to Barcelona's Lionel Messi in that competition.
He won the Ballon d'Or award for a fourth time in December and signed a new deal with Real in November, saying he could continue playing for another 10 years
BBC Sport's Simon Stone
It was billed as Florentino Perez addressing the Ronaldo issue, but when Real Madrid's newly re-elected president gave a round of media interviews, the content was much the same - effectively 'I don't know what is going on'.
He did say Ronaldo is under contract, but everyone knows that. He also said he needed to speak to the Portuguese but, with the Confederations Cup in Russia under way, now was not a good time.
This was a politician's way of addressing a hot topic. Talking but saying nothing.
It merely adds to the air of uncertainty. Does Ronaldo really want to leave Real, or is he angling after a better deal?
Does he want to move back to Manchester United or is his preference Paris St-Germain?
For all the words written and spoken about the four-time Champions League winner, the only people who really know are Ronaldo himself and long-time adviser Jorge Mendes.
They will have the final say. And the wait may be a long one.
This content will not work on your device, please check Javascript and cookies are enabled or update your browser
Real Madrid president Florentino Perez says he has not spoken to Cristiano Ronaldo about his future, but will do so after the Confederations Cup.