Lukaku was left out of the Manchester United squad for the 2-0 win over Perth Glory last weekend because of what was described as a “niggle.”
The Belgian had been doing separate gym work away from his team-mates with Anthony Martial last week amid links with Inter Milan.
But it now seems the Norwegian boss is not prepared to keep Lukaku heavily involved in his plans, all the while talks of a potential exit roll on.
The Baby-faced Assassin left the striker out of the squad to face Leeds United in the final game of their Australian tour before they head to Asia.
Lukaku was pictured arriving off the team bus at the Opus Stadium without a washbag.
There has been talk that Lukaku picked up a knock during training but such speculation is likely to be used as a smokescreen while his future is resolved.
Inter Milan are expected to step up their efforts to sign him as Mauro Icardi’s days at the San Siro look numbered.
The Italian club’s sporting director Piero Ausilio met with United officials last week to try and sound out a deal.
He is said to have been told that Manchester United will not change their stance because their £80m valuation needs to be matched in full.
Solskjaer has since promised to replace the 26-year-old should he leave Old Trafford this summer.
“If we sell players we will have to replace them,” he said.
“There’s never any maximum [number of signings] because there are players here that are coming into pre-season as well that are, ‘I might just have a look at him again because if he has changed as I think he has and it looks like, he might have a career here’.”
David de Gea will also sit out of the clash with Leeds after suffering from illness.
United executive vice-chairman Ed Woodward has stayed back at home in England to work on transfer proceedings.
United are keen to wrap up deals for Harry Maguire and Sean Longstaff if possible.
However they know they face an uphill battle in trying to convince Leicester and Newcastle to reduce their respective asking prices on both players.