The Red Devils came away from the game with a 1-0 win over the Azzuri thanks to Mason Greenwood’s composed finish.
Lukaku, who was the subject of a £54m bid from Inter prior to the game, did not take part in the friendly.
But he seemingly dropped a hint about where he hopes his future lies by holding the blue and black striped shirt as he walked through the mixed zone.
No other United player seemed to be doing so, even if they are likely to have also swapped shirts with their Inter counterparts.
Manchester United are due to head to Shanghai on Monday ahead of Thursday’s game against Tottenham Hotspur.
Former Red Devils striker Dimitar Berbatov believes Ole Gunnar Solskjaer should be trying to keep Lukaku at Old Trafford.
“I think he should stay,” the former Red Devils striker told Sky Sports.
“I like him, I don’t agree with all the criticism he’s getting — yes he has some areas which he need to work like every other player.
“But his teammates need to help him as well.
“For example if I’m a midfield player and I play with him, I will know how to pass him the ball, when to pass him the ball, on which foot to pass him the ball. This is what your teammates need to know, how to play with you.”
Berbatov believes Lukaku is in the right situation to improve however, as his current coach has plenty of experience as a No.9 at Old Trafford.
“I think Ole Gunnar Solskjaer is a good coach for him because if Lukaku wants to ask the coach something, he can go and ask him, because Solskajer was a good striker,” Berbatov added. “So if you need striker’s advice, you go to the coach.”
Inter boss Antonio Conte is a huge fan of the Belgian international and the feeling is very much mutual, with Lukaku recently describing him as the best manager in the game.
“You know very well that I like this player, also in the past when I was Chelsea’s coach and I tried to bring him,” Conte said.
“But I repeat: today Lukaku is a player of United. I have great respect for United.
“I consider him an important player for us to have a good improvement. We know which is our situation; we will see what happens.”