The 'Call My Name' hitmaker, who divorced Ashley in September 2010 after it was revealed he had cheated on her multiple times, does not want Holloway to feel threatened, reported Femalefirst.
"Cheryl thinks it might be a good idea for the pair of them to meet at some point, maybe at the end of the year when things are a bit calmer work-wise.
"Cheryl is still in regular touch with Ashley. 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. She also doesn't want it to become an issue at a later point, especially since she has his surname and no intention of changing it," a source said.
However, the 22-year-old dancer is not too concerned and is keen to meet Chelsea soccer player Ashley, who has not had a serious relationship since Cheryl, 29.
"Tre wants to meet Ashley; he's intrigued by the man Cheryl was married to and remains in touch with," the source added.