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“I just think that that’s something that has been shown with Joe Biden. Father Time is undefeated. Donald Trump is not exempt from any of that,” he said.
Mr DeSantis, 45, said that running the White House is “not a job for somebody that is pushing 80”.
“I will serve two terms, deliver big results, and get the country moving again,” he told CNN.
“That’s what Republican voters want to see.”
He added that, should Mr Trump return to office in 2025, he would actually be older than Mr Biden was when he began his term in 2021.
His comments come as age has become a major talking point among the presidential candidates as well as American voters as the nation gears up for the 2024 race.
Mr Biden turned 81 on Monday and has faced growing questions about his abilities to see out a second term.
The president has taken several tumbles on stage and made repeated gaffes at public events – something his 2020 rival Mr Trump has seized upon, branding him “Sleepy Joe” and claiming he lacks mental competence to lead the US.
Yet, Mr Trump is also 77 and has also faced questions about his health – following a series of similarly bizarre gaffes and unhinged comments.
During his time in office, the former president – who is said to live off 12 diet cokes a day – had a major health scare when he was hospitalised for Covid-19.
As well as their ages, Mr DeSantis told Mr Tapper that he believes Mr Biden will beat Mr Trump if the nation sees a 2020 rematch.
“I wouldn’t be running unless I thought that the Democrats would beat Trump if he were the nominee,” he said, adding that Mr Trump will face a lashing from Democrats if he becomes the GOP nominee.
“You’re gonna see scorched earth. You’re gonna see all this stuff brought out from from the past,” he said.
“The whole election will end up being a referendum on Donald Trump, and Biden will be able to hang out in the basement, and I think he’ll be able to get away with it again.”
Mr DeSantis was once touted as the favourite GOP nominee for 2024 but has been trailing Mr Trump behind in the polls for months – despite the former president facing almost 100 charges in four criminal cases.