"They probably will. The invitation is there," Cyrus told Access Hollywood in an interview. "You know the 'Hannah Montana' film comes out in April. Maybe something might happen around then."
Pressed for details, Cyrus said; "I can't, I can't. I have got to keep a secret."
Hannah Montana, in which Miley Cyrus plays a school girl with a secret life as a pop star, is one of the most popular kids television series in the United States with a huge audience and merchandising empire worth about $1 billion.
Obama has said in interviews that Malia is a big fan of Hannah Montana, but the Obamas have shielded the girls from the media and it remains to be seen whether they will want their daughters to take part in the show.
Miley Cyrus, who turns 16 later this month, told Access Hollywood she did not know for certain if the offer had gone out, but she added: "I think that would be really cool and if anything, have them visit the set."