The TV impressionist will "allow viewers to see the real him" for the first time, according to The Sun.
Bremner joins a list of rumoured celebs, which includes The One Show's Alex Jones, ex-EastEnders star Anita Dobson, actress and popstar Holly Valance and '80s icon Jason Donovan.
14 celebrities will be taking part in this year's series, which will conclude with a final filmed in 3D at the Blackpool Tower Ballroom. At the halfway stage of the competition, there will also be a show filmed at Wembley Arena.
Siberian Latin dancer Pasha Kovalev is the one new professional dancer in the Strictly lineup this year, replacing Jared Murillo.
Strictly Come Dancing launches with a red carpet special on Saturday, Septmeber 10 on BBC One.
> Dolly Parton to play 'Strictly Come Dancing' red carpet launch