Rice was released by the Blues at the age of 14 and has gone on to become a key player for the Hammers, making 126 appearances since his first-team debut in 2015 and earning 13 caps with the England senior side.
Discussing Rice’s potential with talkSPORT, West Ham skipper Noble said: ‘He’s still learning his trade, he’ll get much better with experience.
‘I’m hoping it’s here [at West Ham] but in this game you never know.
‘I’m sure he’ll be a top, top player and an even better player in years to come.’
Noble added: ‘With Dec I don’t have to say too much.
‘He’s such a great kid, got a great family, he’s a top, top player.
‘There are two or three things that I’ve been on him about in the last two seasons to change in what he does.
‘I do believe that if he progresses then he’ll captain England one day. That’s the sort of player he is.
‘He’s such a level-headed kid. You’ve got to remember he’s still only 21.’
Just last month, Rice underlined his ambitions to begin winning major silverware sooner rather than later.
‘As a footballer you only get one career and it goes by very quick,’ he told Sky Sports.
‘You want to be successful for club and country. I think it’s an important thing to win trophies.
‘There’s talk of Harry Kane at Spurs and what he should be doing, obviously he can do whatever he wants. He’s going to win trophies we all know that.
‘I’m only 21 but to get those highs of your career you need to win stuff and that’s what I want to do.’