The midfielder is out of contract in the summer of 2024 and has reportedly turned down a new deal at the Hammers.
The January transfer window is around the corner and no doubt there will be speculation around Rice's future.
But Pearce, who worked with Rice at West Ham, reckons a switch won't happen until the summer.
He told talkSPORT: “He owes West Ham absolutely nothing,” the England legend said. “He’s been brilliant, he’s driven them to two European campaigns.
“I don’t think he’ll be moving any time soon, by which I mean any time before next summer, that certainly won’t be the case.
“But depending on how far England go, if England go a long way in this tournament he’s put himself in the shop window all the time, which is a good thing, you want your players to court attention from elsewhere.
“He’s an outstanding player and what player wouldn’t turn round and say my ambition is to play in the Champions League?
“I’d love to see him drive West Ham into the Champions League but he’s got the world at his feet and I hope he keeps improving.”
Rice admitted while away at the World Cup that he has ambitions of playing in the Champions League.
He said:“One hundred per cent I want to play in the Champions League. For the last two or three years I’ve been saying that.
“I’ve been playing consistently well for my club and I feel like I really want to keep pushing. I see my friends here who are playing Champions League and for big trophies.
“You only get one career and at the end you want to look back at what you’ve won and the biggest games you’ve played in.”