The Belgium as the Blues' man main in recent years, having reached double figures in goals in four of the last five campaigns.
"I know Eden, we came here together and I played against him in France so I have seen him for a long time but, yes, I'm sure he can be the best," Azpilicueta told MailOnline.
"He has that quality of eliminating defenders. It's amazing. But this season he is adding goals and assists.
"Sometimes he was playing very good, but maybe not selfish; he always gives passes to team-mates.
"[Lionel] Messi, Cristiano [Ronaldo], they score 50 goals a year and that is very difficult in England.
"But from his point of view, if he's more aggressive in the box by scoring goals and making assists, he will be the top of his game. In normal play he can create chances. It looks very easy. He goes quick, he scores with both feet.
"Eden has all the qualities to be the best, and his personality as well, the way he behaves. He's the best player in the team, but the way he respects everyone, he's a normal person.
"That's amazing to have the best player and his behaviour and everyone loves him in the club. That's as important as his work on the pitch."