The group will allegedly perform on the final day of the Olympics on August 12 following the global success of their debut album Up All Night.
"The main theme of the Olympic closing ceremony will be celebrating the best of British music, so it's only right that One Direction are opening the show," a source told the Daily Star.
"They are the UK's biggest music export at the moment behind Adele, who is also rumoured to be involved in some way. It's all top secret and the boys aren't allowed to talk about it but they are thrilled."
The insider added: "It isn't every day you get the instant exposure of performing in front of a billion people. One Direction are unstoppable at the moment.
"They have achieved many career highlights at such an early age but this is right up there. To perform in their home country's Olympic ceremony is like winning their very own gold medal."
Meanwhile, The Beatles, Adele, Dizzee Rascal, the Sugababes and the EastEnders theme tune are included on an apparent leaked playlist of songs for the London 2012 opening ceremony.
Watch the music video for One Direction's 'What Makes You Beautiful' below: