For Rice I seem pretty sure about Arsenal but for Romeo Lavia I still haven't heard too much of these rumours because as far as I know he is one of the players that Chelsea and Liverpool are fighting over but not Arsenal.
But it looks like West Ham have turned down Arsenal's offer to take Rice with them next season.
Rice is a player who can provide a lot of good development for West Ham so it is only natural that an offer worth £ 80 million was rejected by West Ham.
Not only you, I also haven't heard too many rumors that Arsenal are eyeing Romeo Lavia, a player with a midfield position from the Southampton team.
Even though 80 million is already very large for this player, it seems that West ham is still reluctant to give this player even though at such a price it has been said to be beyond imagination in their transfer record.
West ham seem to want to play a long game in this regard regardless of how important he is at the moment I feel that him leaving is a sure thing regardless of which club ends up getting it it all depends on the money now talking.
Currently Arsenal are still not giving up and reportedly they have prepared around 100 million to bring in this player because it looks like they still want to continue their hunt for Rice no matter what.