The 25-year-old found himself in the pecking order at Old Trafford last season due to injuries and the emergence of Mason Greenwood.
The academy product has made 16 more appearances than Martial in the campaign that just ended as the Frenchman failed to find consistency.
He has scored just four top-flight goals after getting just 17 Premier League starts by Solskjaer, compared to 21 for Greenwood.
Martial’s hopes of resurrecting his United career appeared to take another hit when Jadon Sancho’s signing was announced on Friday.
United have paid Borussia Dortmund £ 72million for the England international, who will expect to arrive as a first-choice right-winger at Old Trafford.
With Greenwood ahead of him in the pecking order, with Dan James another option on the right, Martial’s time at United seemed to be over.
With his contract until the summer of 2024, Martial is a player for whom United can bring in substantial costs.
While his high salaries prove to be a stumbling block for any movement, the Red Devils are unlikely to want to leave a top earner on the sidelines of their team.
But rather than being on the outskirts of Old Trafford, Martial was given a hint that he could still play a role under Solskjaer.
Martial was left out of the United squad which suffered an embarrassing loss to Queens Park Rangers in Game 2 of their preseason schedule.
Greenwood started up front, with Dan James and Facundo Pellistri selected on the wings as Solskjaer tested a new 4-3-3 system.
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But goals from Charlie Austin and Moses Odubajo along with a brace from Lyndon Dykes saw Mark Warburton’s second division side humiliate the Premier League giants.
As United struggle to find the right combination in attack without their main starters Marcus Rashford and Sancho, Solskjaer has hinted Martial could stay at Manchester.
Speaking after the loss, the Norwegian made it clear his joy at Sancho’s arrival and insisted that United now have one of the best groups of attacking players in England.
“It shows fans that we are serious,” he told Sky Sports, when asked about Sancho’s signing.
“We hope to have one of the best forwards in England for the next 10, 12 years. We have Marcus – 23 years old, we have Mason who is a young boy.
“So we have an English core there and then we have the extra experience with Edinson, Anthony, Bruno, Jesse coming back. So I think the front line is really good.
Martial is currently recovering from the ruptured knee ligaments that interrupted his campaign last season, but he could surprisingly be seen in a United shirt again.
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