England coach Gareth Southgate said the in-form Arsenal defender, who has not featured for England since leaving the World Cup camp in November 2022, had asked not to be considered for friendlies against Brazil and Belgium.
With the European Championship starting on June 14, Southgate had said it would be difficult to choose White over the players who have played for England in friendly games during the international break.
"(White) is a really unique player because he can play three positions," Rice told reporters ahead of England's match against Belgium later on Tuesday.
"In tournaments, that's so key. He can play centre-back, he can play right-back, he can play inverted full-back.
"When I get back I can have a conversation with him and see the ins and outs and see what he thinks. I would love him to come. I think Bukayo (Saka) would. I think Aaron Ramsdale would.
"We're all going to be on him when we get back (at Arsenal after the international break). Hopefully, he can change his mind."
