The Belgium international ended a mixed two-year spell with Manchester United by joining Inter for a reported €80million (£74m) fee in August 2019.
Lukaku has excelled in his debut campaign in Italy, scoring 23 goals in 35 outings in all competitions.
However, the 26-year-old has revealed he almost joined one of Inter's fiercest rivals.
"I was close, really close [to joining Juve], but my mind was always set on Inter and the manager," Lukaku said.
"As a kid I looked up to Adriano, Ronaldo and [Christian] Vieri.
"Obviously when Inter came – and the manager Conte wanted me at Chelsea and Juve as well – I wanted to go there and see what it was like, keep my head down and work."
Lukaku has already bettered his goals tally from the whole of his final season at United, where he fell out of favour under Ole Gunnar Solskjaer.
"One bad year can happen to everybody, and I was done [at United]," Lukaku, who believes he made the right decision in leaving Old Trafford, added. "It was a difficult situation.
"I had to make a decision over going somewhere where I can learn other aspects of my game and work with somebody that wanted me as well.
"Ole wanted me to stay but I told him it was over. I didn't have the energy. All credit to him because he's been a man and he helped me make the move away."
United have steadily improved in Solskjaer's first full campaign in charge following the January signings of Bruno Fernandes and Odion Ighalo, the latter arriving on an initial loan.
"They are going the right way because they are bringing in the right players," Lukaku said. "Ole is doing a good job and the results are good.
"I wish them nothing but the best. As a club they gave me a platform that I had never seen in my life."