The Belgian international striker is on loan at Everton this season but says it is high time he played in continental competition.
"I'm turning 21, I've been a professional for five years already. It is time," he said in Tuesday's edition of the Belgian daily Het Laatste Nieuws.
"It is high time that I play in the Champions League. It is the next step I need in my development. Full stop.
"I still have two years on my contract and I know Chelsea follow my development. In the end it depends on what the manager thinks about me."
Mourinho had previously said Lukaku would need to publicly explain why Chelsea did not keep him but instead sent him on loan for a second successive season, after playing at West Bromwich Albion in the last campaign.
Asked to provide the explanation, the striker told the newspaper: "After the season I had at West Brom (17 goals in 35 appearances), it was important that as a young player I kept developing. That means to play.
"To me there is difference between playing in 20 or 45 matches a season and scoring 10 or 20 goals. Mourinho eventually understood that.
"If I can be better than I was last season, what is then holding me back? Then it will be time to play Champions League football, which is what I want to do."
Lukaku said taking the opportunity of impressing at the World Cup in Brazil would depend on going into the tournament with a "positive spirit".
"You must not go there to play for yourself, to try and force a transfer but to work for the team. The World Cup is our opportunity to show the world we have good players and a good team," he said.
But he also feared that Belgium might not make the impact many feel they are capable of.
"A semi-final might be a bit far. To get to the quarter-finals would be really nice. It is more realistic to speak about reaching the semi-finals or the final of the 2016 European Championship," Lukaku said.
Lukaku, undergoing rehabilitation in Belgium for an ankle injury, said he expected to return to action on March 1 when Everton host West Ham United.
"I don't think I'll have much trouble getting back to my level of play," he said.
- Sports & Recreation
- Het Laatste Nieuws
- Cristiano Ronaldo