The group, who are gearing up to release their new single 'Freedom' next month, said they would like a week on the talent show to be dedicated to the band's back catalogue, which includes seven studio albums and 26 top 40 singles.
"We'd like the Sugababes week on X Factor," Heidi Range told Digital Spy.
"And then we could perform at the end of that week," Amelle Berrabah added.
Thinking about a mentoring role, Jade Ewen joked: "We'd be like, 'Yeah, oh I think you'll find that harmony actually goes like this'."
The trio recently signed a three-album deal with label giant Sony.
'Freedom' is available to download on September 19.
> Watch Digital Spy's interview with the Sugababes here
Watch the Sugababes discuss The X Factor below: