His comments followed the announcement that current hosts Tess Daly and Claudia Winkleman are leaving the show at the end of the current series.
Daly and Winkleman, who have co-hosted the main show since 2014, will make their final appearance together in the Christmas Day festive special.
Daly has presented Strictly Come Dancing since its launch in 2004, with Winkleman joining her on the main show in 2014 after Sir Bruce Forsyth stepped down.
Clifton and Dooley met and won the series in 2018 and now consider themselves "super fans" of the programme.