The pair have been romantically linked since Cole split from her husband Ashley last year. The dancer recently returned to LA having spent time with the Girls Aloud star in South Africa.
"Derek has been like a lovesick puppy since arriving back in LA," a source told The Sun. "He's been talking non-stop about their South African holiday and says he's convinced she's 'the one'.
"He's showing everyone his pictures, which look amazing. He did an entire photoshoot with Cheryl in their hotel room. She did loads of beautiful poses and looks incredible, even without a scrap of make-up."
They continued: "He is convinced they are soulmates and said this holiday made him realise more than ever how well suited they are. He said they'd sit up for hours, chatting until 2 or 3am.
"They spoke a lot about the future and what they both want. He said he feels happier than he ever has in his life, which is a big deal for Derek as he had a pretty tough time growing up."
The paper claims that the 25-year-old is preparing the £400,000 apartment he will apparently share with Cole.
"He's spending the next few weeks putting the final touches to the Hollywood apartment he's bought to share with Chezza when she moves Stateside," the source added. "She's told him what she wants to put her stamp on it and he's obeying her orders."
> Collins 'moving into Cole marital home'