Cole thinks any player would find it difficult to turn down the Chelsea boss.
"I jumped at the chance," England defender Cole said. "He's a great manager. He's proved how good he is with the number of trophies he's won with different teams.
"He's great at motivating players and keeping you on your toes, keeping you doing what you should be doing.
"For me, if there's a player he wants to come to Chelsea, it would be one thought in my mind: to come here and to be under a great manager. It's a pleasure to play under him."