The Olympics heptathlon champion believes that it would be a "brilliant idea" to appear on the show, of which she is a "massive fan".
Speculation emerging over the weekend signalled that Simon Cowell hopes to sign the London 2012 star Ennis along with fellow gold medallists Sir Chris Hoy and Bradley Wiggins.
Responding to the rumours on today's (August 20) Lorraine, Ennis gushed: "This is definitely news to me but it sounds like a brilliant idea. I'm a massive fan of X Factor so we'll see.
"Obviously before the Olympics I was just training so hard and making sure that I didn't miss anything so I had to turn a lot of things down and say no to things that I would loved to have done at the time.
"And now I can just relax now that I've got this medal and I can enjoy myself a bit now."
Both Wiggins and Hoy, meanwhile, have ruled out appearances on the ITV talent show on Twitter.
The original report alleged that ITV had paid £1 million to secure the trio's services - as well as Mo Farah's - for a special edition of the singing contest.
Photo gallery - Team GB's gold medal winners:
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