The 86-year-old TV legend announced earlier that he would be quitting the role of host on the popular ballroom dancing show after a decade.
According to Ladbrokes 51-year-old chat show host Norton is the odds-on favourite to replace Sir Bruce.
Ladbrokes' Jessica Bridge said: "Brucie's retirement has been on the cards for a while, but the odds firmly suggest that Graham Norton will waltz his way into presenting Strictly Come Dancing."
Winkleman, who has been presenting the spin-off show Strictly Come Dancing: It Takes Two between 2004 and 2010, has 3/1 odds of taking the reins as the main show's next host along with Tess Daly.
She stood in for Forsyth last year when he missed an episode after being taken ill with the flu.
William Hill spokesman Rupert Adams said: "Brucie is an iconic fixture in the history of Strictly but given his advancing years, the BBC were always going to have a replacement in mind. Claudia was a great stand in last year while Anton is a massive favourite with Strictly's legion of followers."
Coral have put Du Beke as their favourite (15-8) to replace Sir Bruce followed by Daly's husband Vernon Kay (2-1) and then Winkleman (5-2).
The bookies have also listed Doctor Who and Torchwood star John Barrowman as a potential new Strictly host at 7-2.
However, he will continue to work on pre-recorded Strictly shows for Christmas and Children In Need as well as one-off BBC specials.
"I am very proud of what the show has achieved and confident it will entertain the nation for many years to come.
"I am also delighted that by presenting the Christmas and Children In Need shows I will continue to have a strong association with Strictly," he added.
"In addition, I am looking forward to the specials planned with the BBC as well as some live theatre shows, so before anyone asks, I am not retiring quite yet."