Cheryl, 27, was dropped from the talent competition last month with X Factor boss Simon Cowell saying she would be uncomfortable in the US.
The 51-year-old music mogul had said he offered to give her a place back in the UK show but, when she refused that, he offered to take her back on the US programme, but the Promise This hitmaker turned him down again.
Asked about the situation on ITV's Daybreak today, the 32-year-old former Pussycat Doll said: 'My take is that I was happy to be a part of the show, accept the role of the host, because I believe in Simon, I believe in the X Factor.
'I've met Cheryl only a couple of times and she's absolutely gorgeous and lovely.
'I know she's done what's best for her. And for me it's an honour to be up there, to be able to have a voice and serve as a mentor.'