Lukaku, signed for £75million in 2017, has struggled at Old Trafford and has spent a spell out of the team.
Anthony Martial and Marcus Rashford have flourished in Lukaku’s absence though Manchester United have struggled.
Ahead of the weekend’s action, the Red Devils sit 18 points behind leaders Man City after just 15 games.
They have won just six times, scoring 24 goals in the process and host strugglers Fulham this afternoon (3pm).
It remains to be seen whether Lukaku will return to the starting line-up against the London outfit.
But the Sun report that Lukaku will weigh up a move away from Old Trafford if he continues to be left out of the team.
It’s claimed that Lukaku joins Paul Pogba and Alexis Sanchez in being frustrated at Mourinho, who is under huge pressure.
The former Chelsea boss is the bookies’ favourite to become the next Premier League manager to be sacked.
Reports have grown that Mourinho will move on but his agent Jorge Mendes insists the Portuguese is enjoying life.
“There have been more rumours of Jose Mourinho leaving Manchester United,” said Mendes.
“It’s totally untrue. Jose is very happy at the club and the club is very happy with him.
“He has a long-term contract with Manchester United and is fully committed to the club in building a solid winning project.”
Mourinho explained the reason for leaving out Pogba and Lukaku against Arsenal in midweek.
“Technical and tactical decisions we are going to play with Lingard, Rashford and Martial,” he said before the 2-2 draw.
“We did that already before recently against Young Boys we were not successful in the goals that we wanted to score but we were happy with the situation we created so in that first half against Young Boys we had big chances.
“We believe a combination of these three young fast, creative players even if they are not normally what you call the killer that has a chance, score a goal – we believe in their dynamic and appetite.”