Some bookmakers have named The One Show's Roman Kemp as their favourite for the Strictly job - with Coral cutting their odds.
Actress Hannah Waddingham, Big Brother co-host AJ Odudu, former Strictly winner Stacey Dooley and Celebrity Traitors' breakout star Alan Carr are among the other names being mooted.
Ladbrokes is also offering odds on Holly Willoughby as a surprise frontrunner, with another ITV star, Alison Hammond also on their list.
Whether BBC bosses want to recruit from within the organisation or look to poach stars from rivals remains to be seen.
Caroline Frost, TV editor of the Radio Times, described Daly and Winkleman as "a formidable presenting duo".
Asked if their departure could potentially mean and end to the show, the TV critic told BBC Breakfast there was no need to "throw the baby out with the bath water" and that a "a rebrand" was more likely.
"It still draws in millions of viewers," she said of Strictly. "It's only bad compared with those extraordinary, phenomenal ratings earlier in its reign.
"But certainly it will be like other programmes we've seen before, Doctor Who, Match of the Day, MasterChef; they've all had opportunities for a rebrand... so this could be one of those shows."
