Reports circulated back in April that the glamour model may be joining her boyfriend Leandro Penna on the country's Strictly Come Dancing equivalent Bailando Por Un Sueno (Dancing for a Dream).
The show is known for its adult and occasionally explicit nature during the dance performances.
Price explained to BBC Radio 2 that she will not join the show until sometime next month due to prior work commitments.
She told Steve Wright: "They have asked me. But because of work commitments this month, I will do it, but it will probably be next month.
"They've already started and it's fine if I go on next month. But I can't do it this month."
Leandro Penna made his first appearance on the show earlier this week, but was placed bottom of the leaderboard with his partner Macarena Rinaldi.
Watch his performance below: