Manchester United are eyeing the midfielder, but they face competition from Chelsea who want to get him back on their books having released him from their academy when he was 14.
The England international has reportedly turned down the offer of improved terms and an extension to his West Ham contract twice as he waits to see whether either club firm up their interest.
The London Stadium hierarchy, however, are understood to be relaxed about Rice's future as his current deal has three years left to run.
The Hammers are demanding £100million for his services and and Cole, who played for both West Ham and Chelsea, believes he is worth that fee following his exceptional displays at Euro 2020 for the Three Lions.
He told talkSPORT: "Every time he kicked a ball in the Euros, I was like: 'His price has gone up!'
"He's becoming more and more desirable and for me, he's a top, top player - we all know that at West Ham.
"He's proved himself there and been under the mentorship of a great West Ham legend in Mark Noble.
"He [Noble] hasn't had any caps for England but been a great model pro. Rice has been working under his tutelage and learning the ropes in how to be a leader on the pitch.
"He's got the qualities of a centre-midfielder, but he can play as a centre-back as well. All it is with Declan is that he needs games at the highest level."
Asked whether he was worth £50m, Cole responded: "I'm going double that. In this day and age that is.
"He's so valued by West Ham and an integral part of this West Ham outfit.
"If you start selling your best players then you'll be in trouble."