The Girls Aloud star and her manager will.i.am, who is a coach on the BBC One singing competition, want to showcase the track with a performance on the show, the Daily Star Sunday reports.
Cole's team is said to be finalising her promotional campaign with a spring release in mind and want her to appear on The Voice since it will be directly competing with Britain's Got Talent.
"Cheryl should be releasing her single when The Voice is on TV so it makes sense to combine the two," a source said. "Cheryl's manager will.i.am is obviously a judge on the show so he's already been talking to producers to get the ball rolling.
"The BBC are desperate to beat Cowell and Britain's Got Talent in the ratings and they know there's no better way to do that than by getting Cheryl to perform her new single for the very first time live on the show.
"Cheryl would be a massive ratings winner and scoop for The Voice. Not only will the performance be seen by millions of people, it will also be a good way for Cheryl to stick up a cheeky one finger salute at Simon."
Jessie J, Tom Jones and The Script's Danny O'Donoghue also feature as coaches on The Voice, which is due to premiere in the spring.
Cowell has previously admitted that he views the new show as competition, insisting that he'll make Britain's Got Talent better in response.
Cole and Cowell famously fell out when she was axed from The X Factor USA just days after she joined the panel.
She is said to be considering releasing a song she wrote with Taio Cruz as her new single.
Watch Cheryl Cole's video for 'Fight For This Love' below: