The 22-time Grand Slam winner -- a Madrid fan and honorary club member -- played his most recent tennis match at January's Australian Open and has since been out of action with a hip injury, saying he plans to retire from the sport in 2024.
Perez, 76, has been Madrid president since 2009 and previously held the post between 2000 and 2006.
"Would I like to be [president]? I think so," Nadal told Movistar in an interview on Monday. "I think I'd like to. But there are a lot of things. Right now there's nothing to say because we have the best possible president [Perez].
"What I think today, I might not think tomorrow. There are lots of twists and turns in life. You have to know if you're qualified to do this kind of thing. I'm quite realistic. I know my limitations. I don't know if I'd be capable or not. Time will tell.
"I haven't asked [Perez] about it. I think you [the media] get carried away. I don't think I fulfil the requirements to be [president]."
Madrid's statutes set out a strict set of criteria needed to assume the presidency, which include having been a member for 20 years, being able to personally guarantee 15% of the club's annual budget and holding Spanish nationality.
Nadal has been an honorary member since 2011.
Since returning to power in 2009 following the troubled presidency of Ramon Calderon, Perez has been reelected unopposed in 2013, 2017 and 2021.
Madrid are top of the LaLiga table with five wins out of five and kick off their Champions League campaign against Union Berlin at the Bernabeu on Wednesday.
"Madrid have started well, but it's very early," Nadal said. "There are some important injuries like [Thibaut] Courtois, [Éder] Militao or Vinicius [Junior] ... They also made a spectacular signing like [Jude] Bellingham.
"Another forward would be good," Nadal said. "Am I [waiting for Kylian Mbappé]? Yes I am. I don't have any problem with Mbappé, quite the opposite. I'd be happy if he came ... He didn't have the obligation to come to Madrid when we the fans wanted him to."