Sources told the station that cancer is the mystery illness that prompted the 68-year-old singer to cancel upcoming events and to announce she's taking six months off.
Her publicist hasn't confirmed the reports, but Franklin admitted last week that she had undergone a successful surgical procedure.
Meantime, Franklin's famous friends shared some positive news about her health.
Singer Smokey Robinson said Franklin is doing better since her surgery and is in good spirits.
Robinson said he spoke to pop diva on his way to the Kennedy Center Honors on Sunday night.
Franklin was hospitalized last week in Detroit for an undisclosed health issue that required surgery.
The Rev. Jesse Jackson is also sharing good news about Franklin's health. Jackson said he has visited with her four or five times recently and said she is "recovering very well" from surgery.
Jackson said Franklin takes daily walks up and down the hall of her hospital, and her spirits "are high and her faith is strong."
The Associated Press contributed to this report.