According to the Sun, Palace and Bournemouth are mulling bids for Rice, who is involved in a contract stand-off with West Ham.
Rice broke into West Ham's first team plans early last season and quickly endeared himself to the London Stadium faithful - many of whom have urged Hammers' owners to sort a new deal for the 19-year-old, via Twitter.
And it appears as though Rice is after the same thing, after he 'liked' one such tweet on Thursday afternoon.
West Ham have already added Issa Diop to their central defensive options this summer, and continue to be linked with a move for Alfie Mawson, who also plays in Rice's position, which could prompt the Irishman to consider his options if his situation doesn't change soon.
With former Hammer James Tomkins, as well as Mamadou Sakho, Scott Dann, Jairo Riedewald, Jaraslaw Jach and Martin Kelly all capable of playing at centre-back, Crystal Palace is perhaps not the most obvious destination should Rice leave West Ham.
In contrast, Bournemouth have dearth of options in that department and could potentially offer greater first-team opportunities, with only Steve Cook, Nathan Ake and Tyrone Mings competing for two positions.
Could West Ham lose Rice to Crystal Palace or Bournemouth?