His comments to US magazine The Atlantic came as the country's deposed president Nicolás Maduro was set to appear in a New York court on Monday.
The US accuses Maduro, who is charged with drug trafficking and weapons offences, of running a "narco-terrorist" regime, a claim he denies.
US Secretary of State Marco Rubio has insisted the US is not at war with Venezuela, after air strikes in Caracas on Saturday led to Maduro and his wife being taken into custody and transported to the US.
Some Democratic lawmakers said the operation was an "act of war".
In an interview with The Atlantic on Sunday, Trump said of Rodríguez: "If she doesn't do what's right, she is going to pay a very big price, probably bigger than Maduro."
He added that for Venezuela,"Regime change, anything you want to call it, is better than what you have right now. Can't get any worse".
On Saturday, Trump had vowed the US would "run" the country until "a safe and proper and judicious transition" was possible.
Trump also promised US oil companies would move into the country to fix infrastructure "and start making money for the country".
Despite the US president's claims, Maduro's allies remain in charge.
The Cuban government has said 32 "brave Cuban combatants" died when US forces attacked and captured Maduro and his wife. Cuba - a longstanding socialist ally of Maduro - has announced two days of national mourning.
