De Rossi has impressed as Roma coach since replacing Jose Mourinho in January.
Cole told TMW: "I'm following him, I wish him the best.
Advertisement
Advertisement
"Did I think he could become a great coach when we shared the locker room? Yes, because he always understood football, the locker room. It's very important to have an excellent relationship with the fans and with the players, whether they are young or old.
"He speaks excellent English, he taught me Italian, a wonderful boy, he deserves everything."