David Cameron has suggested there could be further talks about whether the Duchess of Cornwall might become Queen.
While the prime minister said it was "too early for decisions", he added: "I'm a big Camilla fan" and hinted at further talks about her future role.
The official position is that Camilla would be called Princess Consort upon Prince Charles's coronation.
In an interview broadcast on Friday, the Prince of Wales suggested Camilla could become his Queen Consort.
When asked by Sky News whether he was "up for Queen Camilla", Mr Cameron replied: "I think the country is getting to know her and getting to see that she is a very warm-hearted person with a big sense of humour and a big heart.
"But it's too early to talk about these things and I'm sure that it will all be discussed and debated.
"It's too early for decisions about the question you ask, but am I a big royal fan? Yes. And I'm a big Camilla fan too."
In an interview broadcast on Friday - but recorded in August - an American journalist asked a hesitant Prince Charles whether Camilla would become "Queen of England" if and when he became King.
He told NBC: "That's, well... we'll see, won't we. That could be."
When they married in 2005, it was believed Camilla did not want to known as "Queen Camilla".
There was some controversy at that time on the subject. On the one hand, the Labour government said Camilla would automatically become Charles's Queen Consort.
But the Prince of Wales's legal advisers said convention, rather than legislation, dictates whether the wife of the King should be known as Queen Consort.
A series of polls carried out for some of the Sunday newspapers suggests that some of the public do not want her to become Queen.
The News of the World said 2,015 adults took part in its online poll, conducted by ICM Research between 17 and 19 November - after news of Prince William and Kate Middleton's engagement.
When asked: "Do you think the monarchy will be better with Charles and Camilla on the throne, or William and Kate?", 64% replied: "William and Kate", compared to 19% who said "Charles and Camilla".
A separate YouGov poll, published in The Sunday Times, suggested more than half (56%) of people thought William would make a better king than his father, with 15% opting for Charles. The paper said 1,967 people took part in the poll, conducted between 18 and 19 November.
A third poll, published in The People and carried out on the same dates by OnePoll, found almost half (49%) of the 2,000 questioned wanted William and Miss Middleton on the throne, compared to the 16% who opted for Charles and Camilla.