The baker and TV show judge has been approached by bosses after impressing on the BBC Two show alongside Mary Berry, reports The Sun.
Producers are said to be hoping that Hollywood will become a housewives' favourite on the show.
"The Great British Bake Off has been a huge ratings success for the BBC and we are delighted that Paul is now on board," an insider said.
"The hope is that millions of fans who love to watch him and Mary deliver their baking verdicts will also tune in to watch him hit the dance floor. He has a reputation for being a tough cookie and it will be interesting to see how he copes once he is out of his comfort zone."
The Great British Bake Off has continued to rise in the ratings for BBC Two.
Victoria Pendleton recently expressed interest in appearing in the latest series of the dancing competition.
Chris Evans, cricketer Michael Vaughan, soap star Charlie Brooks and Westlife's Nicky Byrne are all rumoured to be taking part in Strictly Come Dancing's 10th series.
In pictures - Strictly 2012's rumoured celebrities: