Lukaku struggled at Old Trafford at the end of last season and has been told Marcus Rashford is ahead of him in the United pecking order.
Inter have been linked with Lukaku, who has not yet played for Manchester United in pre-season.
The Red Devils paid Everton £75million for Lukaku back in 2017, though he has not lived up to the standards expected.
And former United academy player Ben Thornley, who was part of the Class of 92, believes Solskjaer should cash in.
“It may not be a Romelu Lukaku team that he would thrive playing in, but with that being said, he does offer something different with his presence up front, so if he stayed it still wouldn’t be an issue,” Thornley told TribalFootball.com.
“I just feel that Ole Gunnar is moving to a slightly more dynamic and fast forward line.
“I think he proved in his first season that he can score goals.
“I think he scored 27 goals that season. There’s no question that he’s got that ability.
“At Man Utd when you’re challenging for honours you need to have a striker that’s going to be scoring you 25, 27 goals a season and he was the last United player to do that.
“I just think that for whatever reason it didn’t happen for him last season. He just hasn’t hit the heights after that season.
“I’m not too sure that with the way that Ole Gunnar wants to play and certainly the way that he’s indicated that he might play from the preseason games so far, is that with Lukaku’s stature it probably doesn’t fit the style of play that Solskjaer wants.
“I mean, he’s got nimble players up there, he’s got fast players there that are quick off the mark that look like they are going to try and win the ball back up the park if people give them an opportunity to do that.”
Solskjaer has insisted Lukaku has been injured during United’s pre-season preparations.
It’s been reported that the Belgian has not played as United don’t want him to pick up a serious injury.
It comes with plenty of transfer speculation with Inter having already had a £55m bid rejected.