The Belgium international left his homeland for a career in England as a teenager in 2011 and represented Chelsea and Everton, as well as having a productive loan spell at West Bromwich Albion, prior to moving to United in 2017.
At some point the 25-year-old would like to test himself in Italy, but Lukaku insists he is only thinking about his future at Old Trafford for the time being.
Winning is all what matters pic.twitter.com/5E1uLDjOHT— R.Lukaku Bolingoli9 (@RomeluLukaku9) March 7, 2019
"Playing in Serie A is a dream, it would be really a dream,” he told Sky Italia.
"I hope to be able to play sooner or later, even if at the moment I am focused on United."
Lukaku has scored 15 goals for United in all competitions so far this season.