Chalobah was named best afield for this week's Champions League win against Juventus.
Speaking on BT Sport, Cole said: “We watched him in Belfast in the Super Cup and he was outstanding in that game. Thomas Tuchel put him in a big game, I know we don't perceive it as a big game, but to put him in that game against Villarreal, he dealt with it brilliantly. It's great.
“What he's an example of is the academy because he's such a good character and they instill that philosophy and the beliefs into the players from a young age.
“As they get older, they go out on loan, he takes a little bit from his experience at Ipswich, a little bit from his experience at Lorient, little bit working with Thiago [Silva]. It really is like a university for football and then you produce a player like Trevoh who is now playing in the Champions League and not looking out of place.
“He's a great kid. His brother as well would have helped him. He will come into this team and nothing will daunt him.
“My kids have got Trevoh Chalobah on the back of their shirts. They love his hair as well as his footballing ability."