The 42-year-old mother-of-three, who previously presented the dance competition's spin-off show It Takes Two, is said to be taking on the position of co-presenter alongside Tess Daly.
Claudia and Tess, 45, will be making TV history as the first all-female pairing to host a prime-time Saturday night show.
"It will work like the shows that Bruce missed last series," a Strictly insider told the Sunday People. "Tess will be the main presenter with Claudia doing the post-dance interviews.
"This very much fits in with [the BBC's director of TV] Danny Cohen’s desire to be seen to promote female faces during prime time."
The reports that Claudia will co-present with Tess come soon after one of the show's judges Darcey Bussell said "I can't imagine her not doing it."
"She’s been on board for most of the time anyway," said the retired ballerina. "And to have her part of the team is just brilliant.
Tess Daly and Claudia Winkleman
Shortly after Bruce announced that he was leaving the BBC One show, Claudia became the favourite to replace him.
Bruce, 86, confirmed his departure from the show after 11 seasons with a series of tweets on his Twitter account.
"After 10 wonderful years & 11 series, Sir Bruce Forsyth has decided to step down from the rigours of presenting our live shows", they tweeted, before adding: "Sir Bruce is one of the great showbiz legends of our time and our success is due in vast amounts to him. This is not farewell!"