The girl group, speaking after Wednesday night's (January 25) National Television Awards, said they are keen to meet the Syco boss.
Speaking on ITV2, Perrie Edwards told host Caroline Flack: "We haven't met him yet, we really want to meet him. I'd be really nervous - he's so lovely but he'd be really intimidating at the same time."
Of their performance at the ceremony, Jade Thirlwall said: "It's the first live performance we've done since X Factor, so there was a lot of pressure. We were a bit nervous, but it was brilliant."
Jesy Nelson added: "We never get nervous though. Even at Wembley we didn't get nervous. But tonight we were petrified."
Meanwhile, teasing their next single, Leigh-Anne Pinnock said coyly: "Expect something completely different, never done before."
Little Mix's follow-up to their X Factor winner's song 'Cannonball' has not yet been announced.
> Video: X Factor Little Mix plan New Year meeting with Simon Cowell
> NTAs red carpet arrivals - in pictures
Watch David Walliams speaking about working with Simon Cowell backstage at the National Television Awards below:
See a red carpet gallery from the National Television Awards 2012 below: