British government and royal officials are in talks with Iranian authorities about arranging a tour around the fall, the paper quoted a royal source as saying.
It is hoped that Prince Charles trip will help to boost trade and commercial links between the two countries, as well as marking a significant change in Anglo-Iranian relations, the report said.
Britain is viewed with much cynicism because of its colonial past in Iran where the sobriquet old fox is widely used as a reference to the UK.
In a litany of intrigues played on Iran, including a role in 1953 coup against the countrys first democratically-elected government, Britain was seen as the real power behind the peacock throne of a succession of pliant shahs.
Philip Hammond became the first British foreign secretary to visit Iran for more than a decade in August last year and reopen the countrys embassy in Tehran.
The visit came after Iran reached an international agreement on its nuclear program, leading to the lifting of sanctions on the country.
A spokesman at Prince CharlesClarence House office said he was very keen to visit Iran, but the tour was not confirmed yet.
He hopes he would be able to use his role as a diplomat to further encourage the relationship and dialogue between the two countries, the spokesman said.
The prince first traveled to Iran in the capacity of the president of the British Red Cross charity in October 2004 to visit the Iranian city of Bam which was leveled in a strong earthquake.
According to The Sunday Times, Prince Charles hopes to meet President Hassan Rouhani and Iranian business leaders, as well as visiting ancient cities such as Isfahan and Shiraz should the trip go ahead.
Queen Elizabeth, the current queens mother, was the last British royal to visit Iran in 1975, four years before the Islamic Revolution toppled the Western-backed Pahlavi dynasty.
Since then, Iran and Britain have had stormy relations, with diplomatic ties being cut three times.
In Tehran, Hammond said in August that there was no limit to what the two countries could achieve as mutual trust is restored.
Business Secretary Sajid Javid has announced plans to lead what is expected to be Britains biggest-ever trade mission to Iran in May, citing almost unlimited opportunities in the country.
A delegation of leading companies from across the oil and gas, financial services, infrastructure and engineering sectors will reportedly accompany him in the visit.
UK Export Finance, the governments export credit agency, has signed a memorandum of understanding with its Iranian counterpart, the Export Guarantee Fund of Iran to facilitate financing.
By Press TV
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