UK newspaper The Mirror says Cosby, 77, will respond in a month’s time – when he hopes the situation has calmed down.
US shows the Today show or Letterman were likely contenders.
A source said: “He has to address America. It is horrible for him to see his career affected by this.”
Cosby was due to appear on Letterman in mid-November, but the interview was abandoned. It’s unclear who cancelled the talk.