Charles however declined to address the tensions relating to the crisis in the British monarchy sparked by his son Prince Harry, who is stepping down from his royal role with his wife Meghan, the paper said.
“Yes, obviously I would like to [go to Iran],” he was quoted as saying.
“I know that Iran has been such an important part of the world for so many centuries and has contributed so much to human knowledge, culture, poetry, art. I mean, really remarkable people.”
Asked about any future royal visits, a spokeswoman for Prince Charles said: “There are no plans for The Prince of Wales to undertake an official visit to Iran.”
Prince Charles’s wish to visit Iran comes at a time of heightened tensions between Tehran and the West.
A stand-off between the United States and Iran erupted into tit-for-tat military strikes this month, while Britain has called on Iran to release Nazanin Zaghari-Ratcliffe and other dual nationals imprisoned there.
Charles told the Sunday Times he tries to be a peacemaker and that he has prayed for peace in the Middle East.
“I do think the most important thing is a just and lasting peace,” he said in the interview, echoing comments he made on Friday during a visit to the Holy Land.
Britain’s royal family steers clear of politics, though Charles, who will become governor of the Church of England when he ascends the throne, has long spoken out on issues such as inter-faith dialogue and the environment.