The Girls Aloud singer is considering including the track on her debut album, which is due for release later this year.
The 24-year-old beauty's decision to work with the former 'American Idol' judge has reportedly angered bandmate Cheryl Cole, who is also working on a solo LP.
Cheryl - currently the most famous member of the girl group, which is currently on a year-long sabbatical - is said to be worried Nadine's album will outsell hers.
But a record company source has denied Cheryl and Nadine will be competing with each other.
The insider told Britain's New magazine: "Nadine is known as the best singer in Girls Aloud, but Cheryl needn't worry, as the last thing record bosses want is the pair going head-to-head."
Paula has previously penned hits including Kylie Minogue's 2000 single 'Spinning Around'.