In a statement to NBC News on Saturday Clarence House, the office that speaks for Charles, did not comment on Scott's letter.
“All official overseas visits are undertaken at the request of the British Government,” it said.
If the couple do make the trip, it would be the first time a British royal had visited the island.
"A trip of this magnitude by the Crown provides unwarranted legitimacy to a dictatorship with a decades-long history of persecuting and imprisoning its defectors and repressing its people," Scott wrote in his letter to Charles, the heir to the U.K. throne.
"For the sake of standing up for democracy and freedom, I hope you will accept my offer and reconsider a visit to Cuba."
Scott's approach to the Castro regime is consistent with Republican opposition to former President Barack Obama's efforts to normalize relations with the island state after a half-century of estrangement.