Rubio's message explicitly encouraged Cubans to work with the U.S. intelligence agency but did not identify a specific operation or explain what such cooperation would involve.
Rubio, the son of Cuban immigrants, has long advocated for a tougher U.S. approach toward the Cuban government.
The former Florida senator has been a prominent critic of the communist leadership in Havana and opposed efforts to normalize relations without political reforms.
Trump, meanwhile, raised the possibility of U.S. ships stopping near Cuba while discussing Iran during a midterm rally in Fort Myers, Florida, Friday.
"Don't worry. We'll take care of Cuba on our way back from Iran with it. We'll do a little stopover now. We'll do a little stopover," Trump told the crowd.
"Actually, what we're going to do with Cuba is we're going to come back from Iran. Those beautiful ships will pass Cuba. We'll have one of them stop about 50 yards off the coast. They'll raise up their hands."
Trump then suggested Rubio could handle negotiations with the communist-run island.
"And then we're going to send Marco Rubio in to finish up the deal. We'll have Marco. Marco. We don't even have to stop. We could just put him in there and he'll figure it out. He's a great guy."
Trump did not provide details about any proposed agreement with Cuba or indicate whether his remarks reflected an actual military or diplomatic plan.
Fox News Digital reached out to the CIA, State Department, White House and Cuban Embassy in Washington, D.C., for comment.