The NBC talent contest, which has launched to big ratings in America, is apparently being considered by the corporation as their new flagship entertainment show.
According to The Mirror, Cole told a friend yesterday: "I'm very torn about what to do next. This whole thing has been so upsetting. I don't feel like I can even step out the door and face everyone at the moment.
"But I am so grateful to all the messages of support. My fans are giving me the strength to look to the future."
Meanwhile, a source from the singer's record company Universal is quoted as saying: "Universal are heavily involved in recruiting judges for The Voice when it moves to the BBC and they are urging Cheryl to be the big star of that show.
"It would be a fresh start for her and would mean she could work with people who she trusts and who have her best interests at heart. It would also be a great way of sticking two fingers up at Simon Cowell."
The insider added: "She could even do one more series of [the] UK X Factor and then flee to the BBC, such is the demand for her."
Dannii Minogue was also tipped for a role following her departure from the ITV1 talent show, but has since been ruled out.
More on Cheryl Cole and The X Factor USA:
> Cheryl Cole 'X Factor' USA: Where it all went wrong
> Cheryl Cole pictures: From Girls Aloud to 'X Factor'
> Cheryl Cole poll: Should she rejoin 'X Factor' UK?
> Read our latest X Factor USA news