"John Edwards says the story is false," a source close to the former senator told Politico.
The Enquirer claims Edwards proposed to Rielle Hunter three weeks after the death of his former wife Elizabeth, the mother of Edwards' first four children who lost her battle with breast cancer in December.
John Edwards "Grieving Terribly" for Elizabeth
It was the Enquirer that initially exposed the affair between Edwards and Hunter.
Edwards had an affair with Hunter, who was hired to produce web videos for his 2008 presidential campaign. Edwards strongly denied the affair and, subsequently, that he fathered a child with Hunter before eventually admitting to both.
Another source close to Edwards told People Magazine that Edwards and Hunter's relationship is focused mainly on being parents to the child, Frances Quinn, who turns 3 next month.
According to the report, Edwards introduced his three surviving children to Hunter and their daughter Quinn during a holiday get-together at a North Carolina restaurant, expressing hope that they would all "become one big, happy family."