The couple has been spotted openly holding hands and kissing in Mountain Brook, Ala. — where Twitty lives — and at an art show at a nearby art museum. They've also been seen at various restaurants.
Ramsey on Monday denied the reports that they are dating. He said that he and Twitty have a special friendship based on tragedy.
Ramsey's wife and JonBenet's mother, Patsy Ramsey, died last June of ovarian cancer at the age of 49. Twitty was officially divorced from George "Jug" Twitty in December.
Both single parents share the tragedy of children who are victims of unsolved crimes.
Child beauty-pageant winner JonBenet Ramsey was 6 years old when she was killed in December of 1996. She had been beaten and strangled, and her body was found the day after Christmas in the basement of her own home in Boulder, Colo.
JonBenet's parents were the initial focus of the investigation, but they maintained their innocence and said an intruder must have committed the crime. No one was ever arrested and the little girl's murder remains unsolved.
Eighteen-year-old Natalee Holloway disappeared in Aruba while on a high school senior class trip in May of 2005 and has never been found, though she is presumed to have been murdered.
Three different teenaged suspects who lived on the island and were last seen with Holloway were arrested and later released in the case.
FOX News' Carol McKinley and Catherine Donaldson-Evans contributed to this report.