A day after Trump's sanctions on Venezuela, including a stop to vital oil exports to Cuba, contributed to Cuba's latest nationwide blackout, Trump and Secretary of State Marco Rubio both said that the administration sees the island nation as the next country where the U.S. can expand its influence.

"Cuba right now is in very bad shape," Trump said. "And we'll be doing something with Cuba very soon," he added.

Until recently, Trump's comments on change in Cuba might have been considered remarkable. But they come after his administration's military raid that captured then-President Nicolas Maduro in Venezuela and the launch of U.S. military strikes against Iran.

The Trump administration is looking for President Miguel Diaz-Canel to leave as the U.S. continues negotiating with the Cuban government, according to a U.S. official and a source with knowledge of talks between Washington and Havana. No detail has been offered about who the administration might like to see come to power.

Many Cubans do not believe that Diaz-Canel holds much power in Cuba, anyway, as opposed to revolutionary founding father Raul Castro and his family.