According to the official itinerary of Prince Charles's six-day Middle East tour, he is due to meet senior members of the royal family in his 12th official visit to Saudi Arabia on Tuesday (10 February).
Clarence House, however, declined to comment if he will be meeting King Salman and said reports that the Prince will discuss Badawi's case were "speculation".
Badawi, 31, was sentenced to 10 years in prison, 1,000 lashes and ordered to pay one million Saudi riyals (£157,220) for setting up the Saudi Arabian Free Liberals Forum.
Kate Allen, the director of Amnesty International UK, however, said the Prince has a good personal relationship with the monarchy and would be in a position to discuss Badawi's case that has sparked global outcry.
"We don't expect Prince Charles to give up the red carpets and state banquets and become a human-rights campaigner but, as a man who knows the Middle East well, we hope that he will use this visit to pass on a few well-chosen words to his royal hosts," said Allen.
"We still need the UK Government to do more on Raif's case, but Charles's diplomatic intercession could help to secure this man's freedom."
In the first leg of Prince Charles's Middle East tour, he visited a Jordanian refugee camp and chatted with people displaced by the Syrian conflict.
Speaking to BBC, Prince Charles expressed his alarm at the radicalization of young Britons and said: "You think that the people who have come here, are born here, go to school here, would abide by those values and outlooks.
"The frightening part is that people can be so radicalised, either by contact with somebody else or through the Internet."
Charles is also expected to visit Kuwait, Qatar and the United Arab Emirates as part of his six-day Middle East tour.