Lukaku has attracted interest from Inter Milan this summer however has travelled to Australia with United.
Solskjaer had reportedly told the Belgian that he would not be first-choice striker with Marcus Rashford believed to be the Norwegian’s preferred lone attacker.
However it appears that Solskjaer is now keen to keep hold of former Chelsea striker Lukaku.
The Sun report that Solskjaer has told Lukaku to stay at Old Trafford and fight for his place.
It’s claimed the pair spoke before the flight to Australia with the striker being told there is a chance to claim the No 9 role.
Manchester United are still believed to be open to selling Lukaku, though they want to recoup the £75million they paid Everton.
Lukaku’s agent Federico Pastorello had suggested that Inter needed to move quickly if they were to sign Lukaku.
“Nothing new [to report],” Pastorello said.
“We met each other to understand better the situation. We will see what [Inter] is going to decide.
“It is not on us. If the player wants to move [to Inter] they need to hurry.”
Inter are believed to be keen for Lukaku to sign before they face United in the International Champions Cup a week on Saturday.
However the Serie A club insist they are not in a rush.
“The transfer market is a work in progress,” Inter’s CEO Giuseppe Marotta said.
“We are working hard to get the best squad possible for the new season.
“We are ambitious and want the best team possible. We also must find ways to respect all financial perimeters too.
“We cannot rush things because that can lead to mistakes. We have clear ideas but we need to be patient.
“We have important goals and transfer targets in mind.”