The England international said he is enjoying being a regular under manager Manuel Pellegrini and is keeping his focus fixed on the Hammers, per Alec Fenn for MailOnline.
"I signed a five-year contract with West Ham last year, which will keep me at club till I'm 24, and for me this is the best place to be right now.
"I am playing for a manager who has given me my chance and played me week in week out. ... It's all talk until something happens - and nothing has - so I'm just focused on West Ham, doing my best and making fans happy."
Manchester United are "monitoring his development" and could bid £70 million for the 20-year-old in the January transfer window, according to Simon Mullock at the Sunday Mirror.
Rice is a defensive midfielder who has risen to prominence at West Ham and made his England debut against the Czech Republic in March in UEFA 2020 European Championship qualifying.
West Ham highlighted the impact he has made since making his debut for the London club:
West Ham United @WestHam
Two years ago today @_DeclanRice made his debut against Burnley. Since then he has... ✅ Scored the winner vs Arsenal ✅ Won two Young Hammer of the Year awards ✅ Made it into the @EASPORTSFIFA PL Team of the Season ✅ Become a full @England international What a talent! 🤩 https://t.co/FDaCgEgEdf
His performances have seen him draw praise from Manchester City manager Pep Guardiola last season, who has tipped him to have a big future:
Rice spoke to FourFourTwo (h/t MailOnline's Anthony Hay) about reported interest from Manchester United in September. He said: "Don't get me wrong, I think I've got the ability to play for a club like that. But it's all about the timing, and I don't think the timing is right for me at all. I've still got so much to learn."
Manchester United have endured a dismal start to the season and have managed just nine points from their opening Premier League games. They look in need of reinforcements to strengthen their squad and are expected to back manager Ole Gunnar Solskjaer in the transfer market.
The Red Devils "will make up to four signings in each of the next two summer transfer windows," according to Jason Burt at the Daily Telegraph.
Rice may fit the bill given he is young, has plenty of potential and has valuable Premier League and international experience already.
Yet Manchester United's priority in the next transfer window looks to be in attack. The club allowed Romelu Lukaku and Alexis Sanchez to leave in the summer without being replaced and have struggled for creativity and goals in the early weeks of the 2019-20 campaign.