Just two years after arriving from Everton in an initial £75million deal, the 26-year-old is understood to be welcoming interest from the Serie A giants.
Antonio Conte’s side met United in recent days for discussions, but PA understands that Inter have been struggling to fund a deal for the Belgium international.
The striker missed Saturday’s 2-0 friendly win against Perth Glory due to a knock and fuelled speculation about his future as he left Optus Stadium, telling reporters: “You guys will know something next week”.
Lukaku’s brief comment came as Solskjaer faced questions about the frontman’s fitness and happiness at the post-match press conference.
“There’s been so many speculations but, yes, he should be fit for Wednesday (against Leeds),” the United boss said.
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“He trained with the team yesterday, but it wasn’t useful today to risk him, to be fair.”
Quizzed on whether Lukaku will still be a player at the start of the season, Solskjaer added: “Well, let’s see when the season starts. We’ve not had any bids that we’re considering.
“All my conversations with the players I will keep confidential. That’s between us.
“That’s my privilege and I can promise them that I won’t tell (about) our discussions.”