Lukaku cost Manchester United £75m from Everton in 2016, but has struggled to make the desired impact at Old Trafford.
The Belgium international has failed to hold down a regular starting place this season under both Jose Mourinho and Ole Gunnar Solskjaer.
Lukaku, 25, has started just nine league games since Solskjaer took over in December and found himself axed for some of the biggest clashes, including Wednesday’s home defeat to neighbours Manchester City.
Solskjaer has told Marcus Rashford that he is now his No.1 central striker, as exclusively revealed by Starsport.
It has left Lukaku considering his future, with several Italian clubs waiting in the wings to take him to Serie A.
Now Lukaku has added fuel to the speculation he could be set to leave Old Trafford this summer, after admitting joining someone like Inter Milan or Juventus appeals to him.
Inter Milan sporting director Piero Ausilio travelled to watch Lukaku in United’s recent 1-0 defeat to Barcelona in the Champions League.
Inter are considering replacements for Mauro Icardi, who is expected to leave the San Siro this summer, and Lukaku is on their wanted list.
“Playing in Serie A is a dream, it would really be a dream. I hope to be able to play there sooner or later”
Lukaku said: “Playing in Serie A is a dream, it would really be a dream.
“I hope to be able to play there sooner or later, even if at the moment I am focused on Manchester United and fourth place.
“The first memory I have of football is the 1998 UEFA Cup final between Inter and Lazio. When I saw Ronaldo playing, I realized if I wanted to become a professional, I would have to train very hard.”
Lukaku’s agent Federico Pastorello has made it clear the forward is open to leaving United.
He said: “At the moment he is very focused on finishing the season.
“He sees a way to have a career playing in different countries because he would like to win some trophies and prove himself.
“The future is really very open but, at the moment, we don’t discuss about that because really the season is in a big moment.”