The 31-year-old has raced at McLaren alongside Lewis Hamilton since winning the 2009 title with Brawn.
"I've got to drive for two of them, which is great, which as an eight-year-old kid I didn't expect to do.
"As a kid you are very excited about racing for the red team," he is quoted as saying by the Guardian.
"Ferrari is obviously a team I haven't raced for. I've won the world championship and I would love to win the world championship again," added Button.
As a kid you are very excited about racing for the red team
The 9-time Grand Prix winner said recently he would like to finish his career at McLaren, but he now insists: "I don't even know what I'm doing tomorrow. I don't plan too far ahead."
With Fernando Alonso signed up through 2016, the hypothetical seat to be taken by Button is currently occupied by Felipe Massa.
Asked if he can imagine pairing with the feisty Spaniard, Button answered: "It's not teammates I'm afraid of, at all. I love the challenge of teammates.
"Everyone has strengths and weaknesses and it's interesting to work them out. But I don't know what will happen in the future."