The 28-year-old Belgian striker was in excellent goalscoring form for his country at Euro 2020 this summer.
Lukaku scored four times for Belgium and even made UEFA's Team of the Tournament ahead of top scorer Cristiano Ronaldo.
The Inter Milan star successfully converted from the spot-kick against Italy in Belgium's quarter-final defeat at the Allianz Arena in Munich.
However, Lukaku was unable to add to his tally thanks to the tough Italian defence led by Chiellini and Juventus star Leonardo Bonucci.
According to Football Italia, one fan attempted to rattle the Belgium international by asking if he had "finally left Chiellini's pocket, then..."
Lukaku didn't hold back by replying with a savage dig, saying he was "happy" for the user that Italy won the Euro 2020 title.
However, the former Manchester United striker then reminded the user who the 'champions of Italy' were after Inter's title success last season.
Lukaku responded: "Italy won and I am happy for you, truly... but we are the champions of Italy. Inter, remember that."
Football Italia reports that Lukaku deleted the comment, but not before eagle-eyed fans managed to capture a screenshot of the exchange.
Antonio Conte led Inter to their first Serie A trophy in 11 years as they finished 13 points ahead of fourth-placed Juventus in the title race.
The 51-year-old Italian parted ways with the Serie A champions in May amid a dispute with the club owners over their potential financial overhaul.
Lukaku's future at Inter has also remained uncertain after the departure of Conte, despite his current deal with the San Siro outfit expiring in 2024.
The former Everton star has been heavily linked with a sensational return to Chelsea this summer.
Featured Image Credit: PA
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