The Daily Telegraph said the royals chatted up the reality television personality and singer at Whisky Mist, a Mayfair nightclub.
Prince Harry's girlfriend Chelsy Davy, the royals' cousins Princesses Beatrice and Eugenie, and Aguilera's husband Jordan Bratman were also present at the club. Kate Middleton, Prince William's long-term girlfriend, was not, however, the Telegraph said.
To get to Aguilera, the elder prince first had to convince her bodyguard he was who he claimed he was. He is said to have introduced himself by saying: "Er, hi. I'm Prince William, I just wanted to say, 'Hello,'" the Telegraph said.
A witness told the newspaper the pair sat close together and swapped phone numbers.
Hilton was later escorted to the princes' table by a friend.
"Don't you love the princes? They are so hot. I just had to say, 'Hi,'" Hilton told the Daily Mirror.
The Telegraph said Prince William stayed by Hilton's side for most of the night and also was seen exchanging numbers with her.
Swim Week Miami Beach 2014 [PHOTOS]