The relationship between Lukaku, on a season-long loan at Everton, and Mourinho has been closely monitored, since the striker missed a crucial penalty in Chelsea's penalty shoot-out loss to Bayern Munich in the UEFA Super Cup in August.
It is widely believed Lukaku made the move to Goodison Park after a reported falling out with Mourinho on that night in Prague but the Belgian international has stressed that is not the case in an interview with the Daily Mirror.
"Ha! People said there were arguments," said Lukaku, who is a transfer target for both Everton and Tottenham.
"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 proved to be a smart choice by Lukaku, who has flourished under the guidance of Roberto Martinez, scoring 12 Premier League goals though he is still expected to be sold by Chelsea - with the London club hoping to raise enough funds to purchase Atletico Madrid striker Diego Costa in the summer.
"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."
