Speculation has circled around the young midfielder after a breakout season that also saw him earn his first senior England caps.
Manchester United and Chelsea are among the big clubs to have been credited with an interest and Pellegrini was quizzed about what the future holds for the 20-year-old after the Hammers ended their season with a 4-1 win away to Watford.
“It's impossible, I cannot know the future,” Pellegrini said.
“He is, of course, a player who has had a brilliant season, who is 20 years old and an English player who has a lot of qualities.
“Maybe some of the big teams, or all of them, will want him. But that is one thing – the other is whether he will stay here or he goes, and I cannot say at this moment.”
Rice was Players’ Player of the Year and Young Hammer of the Year at the club’s end of season awards after impressing during 34 Premier League appearances this season.
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