Cole was a judge on ITV's The X Factor for three years, with her acts winning twice, but she was axed from The X Factor USA just two weeks into filming the audition phases.
Asked if Cole's upcoming performance on Cowell's BBC rival The Voice would 'be two fingers up' to the show boss, Yates told Heat: "Erm, I don't know. Possibly!
"I think a lot of people want there to be this battle between us and Simon so much."
He added: "It will wind him up. But do I care about that? It's just, whatever. I just think it's wicked that Cheryl's going to perform on our show.
"I think if she comes on and does well, it will be fantastic."
Cole will perform her new single 'Call My Name' on The Voice UK semi-final results show on Sunday, May 27.
The Girls Aloud singer and Cowell reportedly had a falling out after her X Factor USA axe but were said to have made up. Cole recently described Cowell as her 'frenemy'.