Lukaku scored two as United beat Southampton on Saturday, though has regularly struggled at Old Trafford.
The Red Devils bought him for £75million from Everton almost two years ago, though the Belgian hasn’t shown the form that he did at Goodison Park.
Since Ole Gunnar Solskjaer has come in as manager, Marcus Rashford has regularly been preferred, though the Norwegian has played both at times.
But now Express Sport understands that Inter Milan are keen to lure Lukaku to Italy.
And they would be willing to let Mauro Icardi make the switch the other way, with the striker out of favour at the Serie A club.
Icardi has been dumped as captain and hasn’t featured for almost a month.
Inter want their captain to sign a new contract that overrules a current clause that gives him an opportunity to leave this summer.
Icardi knows he will have a two-week window in July to secure a £90m (€100m) transfer to another European giant, before his transfer clause ends.
Inter want to scrap it but his wife and agent Wanda Nara is insisting on a mega pay rise in return.
Icardi currently earns around £75,000 a week at Inter – and could easily double his wages by heading to Old Trafford.
Inter would rather Icardi departed for a Premier League club rather than a Serie A rival.
And the Italian outfit are keen on replacing him with Lukaku this summer.
United are believed to be keen on Icardi as they aim to spruce up their attack for next season.
Lukaku is enjoying life under Solskjaer though and that could prove a sticking point for Inter, and United if they wish to offload the 25-year-old.
Amid rumours that the Belgian could depart Old Trafford for Juventus recently, the striker appeared to hit back on social media.
He posted on Instagram: “When the hate don’t work they start telling lies.”
And after the win over Southampton, Solskjaer praised Lukaku.
“The belief is there, they have gone so long without losing games [domestically] and are raring to go,” Solskjaer said.
“They want to get on the ball and the confidence is high. They were class finishes from Romelu Lukaku and I am so pleased for Andreas Pereira.
“Rom is a goalscorer, he keeps practising every single day and has quality.
“When we changed to two up front that helped him as well.
“We had some great play at times, 3-2 we did it the hard way. That’s why we are turning grey.”
Manchester United are next in action as they play PSG in the Champions League on Wednesday.