Trump DeSantis
File photo: Then-President Donald Trump campaigns with Ron DeSantis at a rally in Pensacola, Florida, on November 3, 2018. Image Credit: AP

Donald Trump escalated his rivalry with Ron DeSantis, warning that he would expose damaging information if the Florida governor were to challenge him for the 2024 Republican presidential nomination.

"If he runs, he could hurt himself very badly," Trump said in an interview Monday with Fox News and other outlets. "I would tell you things about him that won't be very flattering - I know more about him than anybody, other than, perhaps, his wife."

The threat is a familiar move from Trump's playbook to thwart potential rivals. It's also the latest sign that the former president views DeSantis as his chief rival in a potential 2024 GOP presidential primary field. Polls show DeSantis as the strongest challenger to Trump for the nomination should they both run.

"I don't know if he's running," Trump said in the interview. "I think the base would not like it, I don't think it would be good for the party.

The remarks come as voters cast ballots in Tuesday's consequential midterm elections. In Florida, DeSantis is strongly favored to win re-election against Democratic challenger and former governor Charlie Crist.

A message left with DeSantis' campaign wasn't immediately returned.

At an Ohio rally on Monday, Trump said that he would make a "big announcement" - widely expected to be a third White House bid - on Nov. 15 at his Palm Beach estate.

His remarks in the interview with news outlets follows what had been the strongest public broadside yet on DeSantis, when the former president used a Pennsylvania rally to flash polls showing him dominating a potential 2024 GOP presidential field and in which he referred to the governor as "Ron DeSanctimonious."