According to the Daily Mail, the 24-year-old Utah-born dancer visited the UK to watch the show being filmed and is currently in talks about being added to the professional roster on the BBC One show.
Hough previously starred as a judge on Bruno Tonioli and Arlene Phillips's 2007 BBC series DanceX.
He has appeared on four series of Dancing With The Stars, performing with celebrities including Jennie Garth, Shannon Elizabeth, Brooke Burke and Lil' Kim. In series nine he partnered model Joanna Krupa and reached the semi-final stage.
The Strictly final airs on Saturday at 6.35pm on BBC One.