The award-winning musician reportedly declined the offer, citing a busy schedule.
"I'm flattered," The Sun quotes Gallagher as saying. "I'd have done it and all, as I've recently mastered the sticky task of c***** while dancing.
"Sadly though, I'm a bit busy. Maybe next time... "
"Strictly always set their targets extremely high," a programme insider added.
"The show gets huge viewing figures and the bookers behind the show are very much of the opinion, 'If you don't ask, you don't get'. They knew from the off it was ambitious, but they thought it might be something that tickled him."
Strictly Come Dancing is tipped to return to BBC One later this year.
Watch the music video for 'The Death of You and Me' by Noel Gallagher's High Flying Birds: