The singer is apparently still in touch with her ex-husband, who she divorced in 2010, and wants the two men to get along.
"Cheryl thinks it might be a good idea for the pair of them to meet at some point," a source told Reveal.
"Tre hasn't kicked up a massive fuss about it but it's hard for any man if their girlfriend is in touch with her ex.
"Tre wants to meet Ashley, he's intrigued by the man Cheryl was married to and remains in touch with. Tre also finds it tough that Cheryl has no plans to change her surname, even though it's Ashley's."
Meanwhile, the 'Call My Name' star is apparently planning to take Holloway on a tour of Newcastle next weekend.
"She wants him to see where she went to school and the places she used to hang about. She's planned a no-frills few days to give Tre an idea of what it was like when she was young," an insider told The Sun.
Watch the video for Cheryl Cole's 'Under the Sun' below: