Rice would obviously offer good cover and actual competition for Rodri, is young and already an experienced England international. Just in terms of ability + him being homegrown, he is looks like the best Fernandinho replacement out there to me. If he would be willing to accept not being a certain starter and wants to come here, he would definitely improve the squad. Not that bothered if we pay 50m or 90m for Ferns replacement, doesnt really matter if he is here a decade, we are in a position where we can pay the extra to get the man we really want. With that said, we should obviously not pay more than we think he could be worth to us.
My guess however is that he would probably not want a squad role with his next move, and could prefer a move to a club who has a place for him in their starting XI. A move to us seems unlikely based on that + we are unlikely to spend that amount on a position thats not our main priority this window.
For me, a more realistic option would be Kalvin Phillips. 2 years left on his contract this summer as well, good age for a DM, English international and would probably accept being a squad player here. Already plays the position in a system similar to ours (but not at the same level obviously) so I imagine the adaption period to how we play would not be that long. When you combine that with him probably being considerably cheaper in a window our main outlay will be focused on another position, he might be a great option for us. A bit surprised there hasn't been more links between us and this guy, seems like the obvious move to me. Maybe our scouts dont think he has what it takes to succeed here, or have other options they prefer. If thats the case I guess we should trust them.