Hudson-Odoi will be on £100,000 a week if he signs his new deal, with the contract likely to have clauses that can see it match Marcus Rashford's £200,000 a week if he keeps hitting targets.
Lampard says: "That conversation has changed. Too big, too young has gone. What becomes even more important is the attitude of the player, what's around them, how you coach and how you push and drive. That will be part of my job.
"I will have similar discipline, whether you are 18 or 32, but you have to pay a bit more attention to the young lads. For me it will be more how he trains, how he preps, how he is in the gym, how he seems to recover when he's at home and all those things.
"I remember making massive mistakes in what I was eating and what I was doing on a Saturday night when I was 20 years of age. I think now the players are given much more information and that's my job. Most importantly, it's to drive them on the training pitch. When someone has the amount of raw talent that Callum has, the world is absolutely open for him. So that will be my message."