"It's not true," the friend says of a tabloid report that Edwards, 57, has proposed marriage to Hunter, 46.
Although Edwards has neither confirmed nor denied whether he and Hunter are romantically involved, another source close to the former Presidential candidate tells PEOPLE their relationship is primarily about being parents to daughter Frances Quinn, who turns 3 in February.
"The nature of the relationship, as far as I know, is one of a father calling the mother and talking about Quinn, figuring out the holiday schedule," the source says.
Edwards's estranged wife, Elizabeth, died last month after a long battle with breast cancer.
Reporting by SHARON COTLIAR and SANDRA SOBIERAJ WESTFALL