I could see him being cover for Casemiro, closing games at the #8 position when we're ahead and being the backup RCB. I'd turn that down if I was him and just try to go to Arsenal and count on Partey and Xhaka being older, or to Liverpool as Fabinho has played 500 games and appears to have hit the wall physically (and in their system Rice could play as a #8 anyways since they need defensive responsibility to let their fullbacks feck around and create).
But if he did come here and we sent West Ham McTominay, Maguire and 25M, he'd probably do well as Varane, Casemiro and Eriksen's backup and get a lot of games and improve overall as a player. But nobody wants to be James Milner.