The 25-year-old has spent the last two years of his career at the Theatre of Dreams, having secured a big-money transfer from Everton in 2017.
Since then the Belgium international has racked up 95 appearances for United across all competitions, scoring an impressive 42 goals.
However, he has also faced his fair share of criticism during that time, with many fans and experts calling into question his ability on the ball and effectiveness in the final third.
Lukaku has recently found himself playing second fiddle to Marcus Rashford up front under Ole Gunnar Solskjaer and speculation over a summer transfer to Serie A has been rife.
Speaking on Sky Italia's Lords of Football, the Red Devils striker has revealed he harbours ambitions of playing in Italy in the near future, as he stated: "Playing in Serie A is a dream, it would be really a dream.
"I hope to be able to play sooner or later, even if at the moment I am focused on the United."
United are currently sixth in the Premier League with three matches of the 2018-19 campaign remaining.
A 2-0 home defeat against arch-rivals Manchester City on Wednesday has left Solskjaer's side three points behind fourth-placed Chelsea, with Maurizio Sarri's men set to arrive at Old Trafford on Sunday.
The Red Devils have endured a turbulent campaign which is destined to end without a trophy and began with a disastrous five months under ex-boss Jose Mourinho.
The Portuguese coach was sacked in December with the team languishing in mid-table and 12 points off the pace in the hunt for a Champions League spot.
Despite their history, the Belgian is grateful for his experiences under the enigmatic manager, as he added: "I wanted to play [at Chelsea], but Mourinho wouldn't let me and so I left.
"I have never quarrelled with him, but if one thing is not right I am of the opinion that it is better to leave.
"When I found him again he gave me so much, I will be eternally grateful to him."