The threatening statements come even as Cuba and the United States have opened talks aimed at improving their largely adverse relations, which have reached one of their most contentious moments in the 67 years since Fidel Castro overthrew what had been a close US ally.
"I do believe I'll be ... having the honour of taking Cuba. That's a big honour. Taking Cuba in some form," Trump told reporters on Monday as the island faces an unprecedented economic crisis, exacerbated by an oil blockade the US imposed after capturing former Venezuelan President Nicolas Maduro.
"I mean, whether I free it, take it. Think I can do anything I want with it. You want to know the truth," Trump told reporters at a signing event in the Oval Office.
After Trump spoke, the New York Times reported that removing Cuban President Miguel Diaz-Canel from office is a key US objective in the bilateral talks.
Citing four people familiar with the talks, the Times said the Americans have signalled to Cuban negotiators that Diaz-Canel must go but are leaving the next steps up to the Cubans.
Cuba has traditionally rejected any interference in its internal affairs and has considered any proposals on that front a deal-breaker for any agreement.
Diaz-Canel, 65, who succeeded Fidel Castro and his brother Raul Castro as president in 2018, said on Friday he expected talks with the United States to take place "under the principles of equality and respect for the political systems of both countries, sovereignty and self-determination".
But Trump, after removing Maduro from power and joining Israel in attacking Iran, has openly mused that Cuba would be "next".
He stepped up pressure by halting all Venezuelan oil shipments to Cuba and threatening to slap tariffs on any country that sells oil to Cuba.
As a result, Cuba says it has not received an oil shipment in three months and the country has imposed severe energy rationing, resulting in extended power outages. Much of its economy has ground to a halt. On Monday Cuba's electric grid collapsed, leaving the country of 10 million people without power.
On Sunday, Trump told reporters aboard Air Force One, '"We're talking to Cuba, but we're going to do Iran before Cuba".
The White House has yet to detail the legal basis for any possible intervention in Cuba.
