Cole continued: ”He would should stay where he is for a few years because he is one of the main men in the team and that won't be the case if he joins one of the big clubs before he is ready for that.
"Declan is only 20 and the danger of making a move now is that he could become just a number at one of the top clubs and will not realise his potential.
"He should learn his trade properly and West Ham is the perfect stage for him to do that.
"The top clubs will come calling if he is still playing as well as he has done this season a few years down the line, but this is not the moment for him to go to Manchester United or somewhere like that.”
Declan Rice earned an England call-up with his Premier League displays (Image: GETTY)
Manuel Pellegrini is desperate to keep Rice at West Ham (Image: GETTY)
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Rice has made 68 appearances for the club since making his debut in 2015.
The former Republic of Ireland international was named West Ham United Young Player of the Year for both 2016/17 and 2017/18 and Cole is keen for Rice to continue to improve at the London Stadium.
He added: "If you roll the clock forward a few years and he has loads of England caps under his belt after giving plenty of good service to West Ham, then I'm sure they won't stand in his way if a big club comes in for him, but it would be premature for him to make that move now.
"He's had one good season and let's wait and see where he is in a few years time. Declan is a sensible lad and knows that leaving West Ham now would be a risk for him."
Rice has played a key part in West Ham's midfield since making his debut in 2015 (Image: GETTY)