Lampard is pushing the midfielder to sign new terms with his current deal inside it's final 12 months.
He said: “I want him to stay. I want to improve him as a player.
"He can show at Chelsea, the club he came through the academy at, that he is a world-class player. I truly believe that.
“I am not going to say, 'This is all going to be your way'. But knowing his talent, he can be central to this team and he can be central to an England team.
“I remember being 17, 18 or 19 and I wasn't as good as Callum at that age.
“When someone has the amount of raw talent that Callum has, if he drives and pushes, then the world is absolutely open for him."