Lukaku has agreed a £180,000-a-week deal with Inter ahead of the proposed move, according to The Sun.
The Belgian striker would be allowed to leave Old Trafford for around £75m – the same fee Manchester United paid Everton in 2017.
Lukaku is hoping to move to Italy to get his career back on track under Antonio Conte’s tutelage, it said.
If the deal goes through, it’ll be very good business for United, claimed TalkSport’s Ben Fletcher.
“Romelu Lukaku is reportedly off to to Inter for £75m, and £180,000 a week,” he said.
“That’s a very, very good deal for Manchester United.
“£75m for that player, if true, is an absolute touch for them.”
Lukaku held talks with United last month too discuss his future, after Ole Gunnar Solskjaer told him he would be playing second fiddle to Marcus Rashford next season.
But United would only let him go elsewhere if they get back the money they spent on him two years ago.
Jose Mourinho, who was manager of United at the time, bought Lukaku for £75m from Everton, despite interest from Chelsea.
Inter boss Conte was manager of Chelsea when the Blues were interested in signing Lukaku.
Belgium manager Roberto Martinez would welcome Lukaku’s move away from Old Trafford, as he said the striker needed to find the right club.
“I think the situation is quite clear,” Martinez told Belgian newspaper Het Laatste Nieuws.
“Romelu Lukaku and Manchester United have spoken to each other. It’s been quite open that a move would be beneficial for both parties. The next step is to find the right destination.
“Romelu is ready for something new. I’m not worried about ‘Rom’.”
Lukaku has made 66 Premier League appearances for United over two years, and has scored 28 goals.