Yesterday, Ross announced that he is leaving the BBC after 13 years with the corporation. It was later reported that the presenter was forced out.
Norton, who earlier this week signed a £4 million deal to stay with the broadcaster, is being listed by the bookmaker as 1/6 to replace Ross.
Comedian Michael McIntyre is behind him at 9/1, closely followed by Live From Studio Five host Ian Wright at 12/1. Paul O'Grady and Harry Hill are 14/1 each, while Chris Evans has been placed at 20/1.
Other famous faces in the frame include Simon Amstell at 20/1 and Ricky Gervais, Russell Brand and Terry Wogan at 25/1 each.
> Norton 'no match for Jonathan Ross'