The Times newspaper said a source had heard Charles express opposition to the policy several times in private, and that he was “more than disappointed” by it.
The comments were reported after a High Court ruling paved the way for the first flight to the east African country to go ahead on Tuesday.
A Clarence House spokesman said: “We would not comment on supposed anonymous private conversations with the Prince of Wales, except to restate that he remains politically neutral. Matters of policy are decisions for Government.”
As head of state, Charles’s mother the Queen has to remain strictly neutral with respect to political matters and does not vote or stand for election, the royal family’s official website says.
Traditionally, royals do not become involved in political matters.
However Charles, a future king, has been outspoken in the past and faced criticism over his involvement in public and political issues.
In 2015, Charles had to defend his decision to write a series of letters to government ministers, some of which are known as the “black spider” memos, so-called because of his use of black ink.
At the time, Clarence House said the correspondence – on issues including a lack of resources for armed forces fighting in Iraq, the benefits of complementary medicine, and the need for affordable rural homes – showed “the range of the Prince of Wales’s concerns and interests for this country and the wider world”.
In the same year there was controversy when it emerged Charles had been routinely receiving copies of confidential Cabinet papers for more than 20 years.
As well as the Queen, it included the Prince of Wales, although it was not suggested he had requested access. Heirs to the throne were believed to have been included in the group since the 1930s.
In a BBC documentary to mark his 70th birthday in 2018, Charles said he would stop speaking out on issues when he became king, saying he was “not that stupid” to continue what some had termed “meddling”.
The prince acknowledged he would not be “able to do the same things I’ve done as heir”, and as monarch would have to operate within “constitutional parameters”.
Former BBC royal correspondent Peter Hunt said there is a risk is of “an opinionated prince morphing into a meddlesome king”.
Writing in The Spectator, Mr Hunt said that in the latest instance regarding Rwanda, despite the statement from Clarence House, Charles has not been neutral in making the reported comments.
Mr Hunt added: “A man teetering on the edge of inheriting a unifying role as Head of the Nation has entered a divisive debate very firmly on the side of Boris Johnson’s opponents.
“One day those occupying the roles of Prime Minister and Home Secretary will be devising immigration policy as members of His Majesty’s Government.”
Fellow royal commentator Jennie Bond praised Charles for speaking up, albeit privately.
She told GB News: “He’s not the monarch, he is the Prince of Wales and I, for one, woke up this morning and saw those headlines and thought ‘Good for you, Charles. That’s just great. You’ve come out and you’ve said what you think’.”
She added that, given that it has been reported Charles made the comments several times, “he probably wasn’t averse to his views being aired publicly” and that he “probably knew it would get out”.
In 2020, Buckingham Palace appeared to distance itself from comments made by Charles’s son, the Duke of Sussex, as Harry urged people in the US to “reject hate speech” and vote in the presidential elections.
Harry faced a backlash amid claims of political interference and suggestions he was telling people to vote against Donald Trump.
Although UK law does not ban royalty from voting, it is considered unconstitutional for them to do so.
Buckingham Palace highlighted the fact that Harry was no longer a working royal, and said his remarks were made in a “personal capacity”.