The 24-year-old is widely expected to leave the Hammers this summer, with Arsenal, Chelsea, Manchester United, Liverpool, Newcastle United and Manchester City all thought to be keeping tabs on him.
Speaking at the 2022 World Cup, Rice suggested that he would be looking for a move away from the Hammers in the near future, as he wants to challenge for "big trophies".
"One hundred per cent I want to play in the Champions League," Rice told reporters in Qatar. "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. I really want to do that."
The Englishman has entered the final 18 months of his contract at the London Stadium, and there have been reports that West Ham are open to selling him for around £100m this summer.
Noble, who hung up his boots at the end of last season before becoming a staff member with the Hammers, has admitted that the club's star player could be on the move in the near future.
"It's just the world we live in. We're West Ham and these players want to go out and play Champions League football - and do you blame them?" Noble told the Evening Standard.
"Dec is no different. Dec will always be hailed at West Ham as a fantastic player and such a top, top person. But I don't think anyone begrudges him wanting to go and win things. We just hope he'll keep performing like he has been over the last month or so.
"Wherever Declan ends up, or however much someone pays for him, whether it's here or anywhere else, he's worth every penny.
"He's said openly he loves playing at West Ham, but he has got ambitions as a player to go and play in the Champions League and win trophies. I don't think any West Han fan can actually have an agenda over that.
"Do you blame him for having really big ambitions? Of course you don't. If he didn't, he probably wouldn't be as good as he is."
Rice has again been a key player for West Ham during the 2022-23 campaign, making 27 appearances in all competitions, contributing one goal and three assists in the process.
Man United are believed to have failed with a £100m offer for Rice last summer, with the Hammers said to be looking for a fee of around £120m plus add-ons for his services ahead of the 2022-23 campaign.