According to the Sunday Mirror, BBC bosses are keen to get Bruno on the show for the upcoming eighth series, following the popularity of boxer Joe Calzaghe last year.
"Frank is one of the country's best-loved celebrities. He is still very fit and trains every day so the gruelling schedule of Strictly wouldn't be a problem for him," said a source.
"The producers have made getting Frank onto the show their number one priority."
Bruno, 48, was the world heavyweight champion in 1995 and became well known after retiring from the sport for his appearances in pantomimes around the UK.
Last year, a friend of the ex-boxer claimed that the BBC has snubbed Bruno for the seventh series.
Rugby star Gavin Henson, actresses Patsy Kensit and Felicity Kendall and politician Anne Widdecombe have all been linked to upcoming run of the BBC dance show.