Moyes has overseen much of Rice’s development over his two spells in charge at the London Stadium.
He said: “I’ve been here twice. On the first occasion, he was a young boy making his way playing centre-half most of the time.
“Since I have come back he had already developed into a midfield player.
“I think in the last two years he has stepped up his leadership, his playing. I think everybody would see him as an England player at the moment.
“A couple of years ago, he was still developing into an England player. I think about how well he has done for the national team, but more importantly you don’t get recognised for the national team if you don’t play well for your club side.
“Declan has played really well for West Ham. I think he can keep moving on.
“I think he’s got little bits of his game he can add to and we are at him all the time to keep improving, to keep driving the team on and show those leadership qualities which I think he’s already got for a young man, but they will get better as he gets older as well.
“Being captain of West Ham is a big deal when you look at the great captains at this club over the years, none more so than Mark Noble He has a role model to look up to in Mark Noble and we hope that Declan can keep carrying it and improving.”
If West Ham want to keep hold of Rice in the long-term, the challenge for Moyes is to continue bringing in quality signings to play alongside him and boost their bid to reach the Champions League.
The Scot wants a defender and a forward this month but, as in previous transfer windows when he landed Tomas Soucek, Jesse Lingard and Kurt Zouma late on, Moyes is having to bide his time to get the right player.
“I would like to bring some new faces in if I could to add to the group of players I have got,” he said. “But we will try and do it as well as we can.
“At the moment the ones we are looking for or the ones we would like to get are either not available or we just can’t get. We will keep looking and see what we can get between now and the end of the window.
“I am really keen to add to it, the board are with me they want to add as well, they are supportive.
“So it’s actually trying to identify the right players and bring in players who we would really like to bring here and go on the rest of the journey, so we will keep looking and hopefully something will appear for us in the last couple of weeks.”