Mount impressed under Lampard last term at Derby County and has taken that form into preseason.
He said: “There are no promises. Not a chance. You have to prove yourself.
“He's said that before, that it doesn't matter if you're young or old, if you're ready to play, he's going to play you. It's exciting times but there's no given.
“Even if you've been at Chelsea since a little boy, it doesn't matter. Look at the squad and there's world-class players there.
“So for me, as a young player, I've got to work hard in training, prove I can play.
“But I'm learning from these players and that's best for me. I'm working hard to prove to the manager I can step up and play."
Mount has also taken a leaf out of Lampard's book with extra work after training, something the new gaffer did daily as a player.
The youngster added: “Last season, he would always speak to me about doing free-kicks after training and extra shooting.
“So I'd always go to him after training and say, 'Can we do a few shots and free-kicks' just to work hard.
“Everyone thinks you don't worry about what happens off the pitch but that's one of the main things, in the gym, on the training pitch after training.
“If you can get that extra percentage that's the main thing."