The relationship between Lukaku, on a season-long loan at Everton, and Mourinho has been closely monitored since the striker missed a crucial spot-kick in Chelsea's penalty shoot-out loss to Bayern Munich in the Super Cup in August.
|2/7||Chelsea are 2/7 with Bet365 to beat Stoke this weekend|
"Ha! People said there were arguments," Lukaku told the Daily Mirror.
"There were arguments in the press and stuff but I don't know where it came from. I just spoke to him and said hopefully what I wanted as a player and he was okay with it."
Lukaku was expected to stay at Stamford Bridge this season to cover for Samuel Eto'o, Fernando Torres and Demba Ba but he was determined to continue his development elsewhere.
It has proved to be a smart choice by the 20-year-old, who has flourished under the guidance of Roberto Martinez, scoring 12 Premier League goals, though he is still expected to be sold by Chelsea this summer, with the London club hoping to raise enough funds to purchase Atletico Madrid striker Diego Costa.
"I had the opportunity to go," Lukaku said.
"The feeling I had after three games at Chelsea, I was really hoping for a starting spot because of the season before when I had scored goals.
"But it's a big club, there is real competition and they said there was a feeling I had to stay patient again.
"And the feeling that I had from my first year came up again and I knew I had to go. Because how you could be on the bench after the year I had last year? Because I still want to progress. I don't want to be a one-season show.
"As a youngster, you normally have to play. How will you be one of the best not playing? Look at (Wayne) Rooney, (Cristiano) Ronaldo, (Didier) Drogba - every top striker. They always played.
"They played constantly, always, all the time. Games, games, games. I just want to be one of them - that is my ambition, I just want to be one of those guys, I don't play football to show off or to make money, I play because of my pride and because I love the game."