The former England international believes Carroll has the ability to match the Ivorian.
"I played with him at Liverpool and West Ham and the player that is at West Ham is full of confidence, energy and aggression, and everyone can see what a good player he is," Cole told The Sun.
"He had a difficult time at Liverpool but the West Ham Andy Carroll is a real handful and a top player. he'll be looking at getting himself in the England squad now.
"He can be anything he wants to be. You can look at a Drogba, that's the level he can get to."