The Belgium forward, who impressed on loan at West Brom last term, has scored in each of Chelsea's pre-season friendlies so far, with a goal in Bangkok and another in Kuala Lumpur on the tour of Asia.
"I am confident in my qualities and I am just keeping going like I have been doing," Lukaku said.
"I can score more goals, I can get more assists. I can do more for the team.
"He is the manager and he has a vision of the way he wants to play.
"The players have to improve to do that. I certainly have it in me.
"He is very direct - and I love that. It is important. If he has something to say to you, he says it. That is a good thing.
"He is very direct and in your face."
Lukaku would welcome the competition provided by Wayne Rooney if Chelsea can persuade Manchester United to sell them the striker.
"You know when you are playing for a team like Chelsea, there is going to be competition," Lukaku added.
"It is the manager's choice. You have to accept that you have to work hard to make it a successful squad.
"If he is part of our team I will welcome him with open arms."
Mourinho is building for the future and expects Nathaniel Chalobah to be part of it.
Chalobah spent last season on loan at Watford and will be allowed to go out on loan for one final campaign before returning to challenge for a place in the Blues' first-team squad.
Mourinho said: "He is a very, very good player. I like him very much. Very, very much. I am very impressed.
"For sure, a Chelsea player (in future), for sure. We think he is there.
"He could be in our squad already. But we think one more season and it will be his last one out on loan.
"We will see whether or not it is a Premier League club."
Mourinho also intends to send Josh McEachran, Lucas Piazon and his fellow Brazilian Wallace out on loan for the forthcoming campaign.