The Hammers midfielder has shot to prominence in a short space of time after forcing his way into Manuel Pellegrini's side last season, while he is also in the thoughts of England boss Gareth Southgate.
Rice's form has caught the eye of the Premier League's top clubs with United linked on a number of occasions, while Manchester City are also said to be in the hunt.
The rumours look sure to rumble on and it is only going to be a matter of time before he does move on to a club who will be challenging for titles and silverware for years to come.
However, he is just 20, and appears to be in no rush to move away from the London Stadium, where can continue to develop before one day getting his dream move to one of the big boys.
Many players in Rice's situation would jump at the chance of a move to Old Trafford, but the youngster has suggested he would have turned them down had an approach been made over the summer.
Rice is not short of confidence and believes he could have slotted straight into Ole Gunnar Solskjaer's midfield, but says the timing would not have been right.
"Don't get me wrong, I think I have got the ability to play for a club like that," he said of the United interest. "But it is all about timing and I don't think the timing is right for me at all. I have still got much to learn.
"I've signed a contract here for the next few years and I'm looking forward to playing this season and the season beyond, so we'll see where it goes. To be called a West Ham legend in the future, maybe, would be a real honour."
Rice is certainly saying all the right things and his words will be music to the ears of the Hammers fans, who have already taken to him in a big way.
If he hangs around for a few years and carries on giving his all for the club, then there will be no complaints if a club like United come along and he decides to take the next step.
Rice has played every Premier League game so far and will be one of the first names on the team sheet as the Hammers look to break into the top six this season.