The England international spoke to FourFourTwo (h/t MailOnline's Anthony Hay) and was asked about the links to Old Trafford this past summer:
"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.
"I'm loving it at West Ham. The connection between me and the supporters is special. I've become one of the fans' favourites and the manager likes me.
"It's the best place for me to play my football."
He added he's looking forward to spending his near future at West Ham, indicating he's in no rush to leave his current club.
A former member of Chelsea's academy, Rice has been with West Ham since 2014 and has increased his reputation in the past few seasons.
After formerly turning out for Republic of Ireland's various youth teams, as well as three friendlies with the senior squad, he has become a regular part of England's setup since making the switch. Rice was once again called up for the qualifiers against Bulgaria and Kosovo:
The switch to West Ham has proved a fantastic decision, and Rice committed his future to the club in December of last year by signing a long-term deal.
That hasn't stopped the speculation, however, as he has continued his development into one of the Premier League's best midfield prospects.
His young age, tremendous upside and senior experience would seemingly make him an ideal target for United, who signed two similar-age players in Aaron Wan-Bissaka and Daniel James during the summer.
Rice also plays a position of need for United, who have been overly reliant on Paul Pogba early this season. The France international has been kept busy:
Pogba has mostly paired with Scott McTominay in midfield, and while the Scotland international is a solid prospect in his own right, he's not nearly as disruptive as Rice. Per WhoScored.com, the latter averages 3.5 tackles per match, compared to just 1.5 for McTominay.
As United continue to build their squad into a title contender, a bid for Rice in January or next summer would seem logical. The midfielder appears happy to stay in east London and continue his development in familiar settings for now, but his rise to stardom would suggest he could be ready for the switch to a top club soon.