Mr Trump was speaking to rightwing talk show host Glenn Beck when he made the comments about the tech entrepreneur and author of Woke Inc.
The ex-president said Mr Ramaswamy, 38, could be a “very good” choice for vice president, but warned him that he may need to pull back on some of his more controversial statements.
“He’s a very, very, very intelligent person. He’s got good energy, and he could be some form of something,” Mr Trump said on BlazeTV. “I tell you, I think he’d be very good.”
But he added: “He’s starting to get out there a little bit. He’s getting a little bit controversial”.
“I got to tell him: ‘Be a little bit careful. Some things you have to hold in just a little bit, right?’” Mr Trump told Beck.
Mr Ramaswamy has outlined similar policy visions to Mr Trump, such as closing down the Department of Education and using the military to take out Mexican drug cartels.
The entrepreneur has also pitched the idea of ending the war in Ukraine by freezing the current battle lines and allowing Russia to take control of the Donbas if Ukraine ends its efforts to join NATO and Russia severs ties with China.
Appearing at an event in Iowa, Mr Ramaswamy said the US should protect Taiwan against China “at least until we have achieved semiconductor independence in this country, at which point we will reevaluate”.
During the first Republican primary debate on 23 August, former UN Ambassador Nikki Haley argued that Mr Ramaswamy wanted to “stop funding Israel”.
“Our relationship with Israel will never be stronger than by the end of my first term,” Mr Ramaswamy replied. “But it’s not a client relationship, it is a friendship. And you know what friends do? Friends help each other stand on their own two feet.”
During an appearance on British comedian Russell Brand’s programme on Rumble, Mr Ramaswamy said that when the $38bn aid package to Israel expires in 2028, the country would not need additional support.
“You have no foreign policy and it shows!” Ms Haley shouted at Mr Ramaswamy during the debate following his suggestion to end the funding of Ukraine. “You don’t do that to friends. You are choosing a murderer over a pro-American country.”
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