Prince William made the comment when asked how many children he would like, during the second day of the couple's Diamond Jubilee tour to Singapore.
A teenager at one walkabout said the prince had responded by saying "he was thinking about having two".
The Duke and Duchess of Cambridge also said they would like their "superhero superpower" to be invisibility.
The prince, who married Catherine Middleton in April last year, has spoken before about starting a family, but has not mentioned numbers.
After the couple's visit to the Gardens by the Bay attraction, Corine Ackermann, 17, said: "Someone asked him how many children he would like to have, and he said he was thinking about having two."
Jaz Heber Percy, 13, asked the prince what superpower he would like to have if he could be a superhero.
The prince replied: "That's a hard question - I'm not sure. I'll have to think about it. I think invisibility."
The duchess had agreed that she would need to be invisible too, "otherwise he would be able to sneak up on her," Jaz said.
Several people in the 1,000-strong crowd fainted as they waited in sweltering heat for three hours to see the royals.
Local children who had been given the morning off school chanted: "Will, you're brill. Kate, you're great".
The royal couple planted a Pachira glabra variegata tree to mark their visit.
They also visited a Rolls-Royce jet engine factory, where the prince praised the "cutting-edge aerospace technology developed by one of the United Kingdom's great global companies".
During the visit, the duchess fitted the last of 24 fan blades to a Trent 900 engine.

James Kelly Nestruck said he received a contract between Wests Tigers forward Martin Taupau and the Manly Sea Eagles.
The two clubs have confirmed the transfer.
A possible explanation for the mix-up is that Mr Nestruck has the same initial and surname as the CEO of the Sea Eagles, Joe Kelly.
But in a statement the Wests Tigers denied that they had sent the email.
Mr Nestruck made light of the incident on his Twitter account, having become an unlikely trending topic in Sydney.
"Hey there Antipodean rugby enthusiasts... Thanks for all the interest, but I'm done playing at Kiwileaks now - and am off to review a play," he said.

The centre said all 200 tickets to see Brumm, Maja and Brumma were booked within 15 minutes of being made available on Thursday.
The bears are 22-month-old siblings and arrived at the centre at the end of November from Kolmarden Zoo in Sweden.
Visitors will be able to see them from 4 January.
The new arrivals join Star, the centre's resident female bear.
Comet, the centre's other European brown bear, died in August aged 30 after a short illness.
A Leisure & Culture Dundee spokesman said: "We have been absolutely blown away by the response to the preview.
"We are really excited about introducing the bears to visitors in the New Year and early indications suggest they are going to be incredibly popular."
The Duke of Cambridge has reportedly revealed he would like to have two children with his wife.
[NEXT_CONCEPT]
A Canadian theatre critic has said he was accidentally sent an email revealing that a rugby league star is switching clubs in Australia.
[NEXT_CONCEPT]
Staff at Dundee's Camperdown Wildlife Centre said they have been "blown away" by demand for preview tickets to see its three new European brown bears.