At 19, Cole is two years older than the Everton sensation - but the Blues' 6ft 3in frontman has one big advantage over his Merseyside rival.
And that is the presence of genuine class around him in the forward line, with Dutchman Hasselbaink, Icelander Gudjohnsen and Italian Zola offloading their wealth of experience on another bright young English hope.
Cole knows Claudio Ranieri has "big plans" for him - and the boss could now hand him his first league start of the season against Birmingham at Stamford Bridge on Saturday due to Hasselbaink's groin injury and Gudjohnsen's ankle problem.
Cole, who scored both goals in Wednesday's 2-1 Worthington Cup victory against Gillingham, said: "I'm not a natural goalscorer, but someone like Jimmy is.
"I used to play in centre midfield so I've had to adapt. And I've been taught at Chelsea.
"All the staff have helped me. I practice trying to take the ball around Carlo Cudicini, who is one of the best goalkeepers.
"It gives you inspiration just looking at the players here. You have to better yourself and try to be as good as them. I'm learning off all the strikers. They're giving me tips all the time."
Cole's hairline fracture to the fibula in his left leg prevented him following up the brilliant goal he came off the bench to score in the first game of the season against Charlton.
"When I got the injury, the boss kept on checking up on me - how long the injury was going to take, whether I could train," said Cole, who could keep his place alongside Zola.
"And then the manager has put me straight back into the team. You just think 'Yeah, he's got big plans for me'.
"I like all the attention but not too much of it because it puts pressure on you. I'm a really cool person, down to earth. I've just got to keep it real."
Asked about his injury and Rooney, he added: "I felt bad about it because I was doing really well and then Wayne Rooney came along and took all the headlines.
"I just thought I'm going to have to do even better when I come back. He's done really well and it's always good to see youngsters coming through.
"He's one of the best. It gives me inspiration because I'm a youngster myself and it's hard to come through at a club like Chelsea."