Speaking on "Sunday Morning Futures" on Fox News, Mr. Trump suggested businessman Vivek Ramaswamy or Sen. Tim Scott (R-S.C.) could be his running mate. So far, Mr. Trump has directed his criticism toward Florida Gov. Ron DeSantis in the GOP primary, while Mr. DeSantis has suggested that he wouldn't want to be Mr. Trump's vice president in a recent interview.

When asked by Fox host Maria Bartiromo about whether his running mate could come from the Republican 2024 primary, Trump said, "Possibly."

"I think Vivek has done a very good job, frankly. I think some others have done a good job," the former president said. "You have some good people on the stage actually. I think you have some very talented people," he also said. "I've been impressed by some of them. Some of them I'm very friendly with, actually."

He added that "I think you have good potential Cabinet members, too," without specifying.