The 22-year-old has been in impressive form for the Hammers during the 2020-21 campaign, while he is widely expected to be part of the England squad for this summer's European Championships.
However, White has claimed that the club's owners value Rice, who has also previously been linked with Chelsea, in excess of £100m.
"[David] Sullivan has already told me it's got to be north of £100m or they won't entertain it. We'll wait and see what happens with that," White said on talkSPORT.
Rice has scored once and provided one assist in 28 appearances for the Hammers this term.