Speculation is increasing that the Red Devils would not necessarily show their manager the exit door if they are forced to make a change at the top in the coming weeks.
The Manchester giants are just two points off the drop zone in the Premier League and have the unenviable task of hosting Liverpool at the Theatre of Dreams this coming Sunday, with Jurgen Klopp's side boasting a perfect league record and sitting pretty eight points clear at the top of the table.
Solskjaer reportedly warned his players they could cost him his job if they don not manage to get a result against their bitter rivals, having managed to take just 17 points from his last 17 games in charge.
The Norwegian, however, who would be entitled to a year's salary from United if he were to be axed - worth around £6.5m - could yet be thrown a lifeline to stick around at his beloved club.
There has been chatter during the international break that United's top-brass would be loathe to sack a club legend like Solskjaer, so could instead offer him a job "upstairs".
That could even entail the likeable 46-year-old being offered the director of football role, which United have been looking to appoint for the past 18 months or so.
United have sounded out a number of top names on the continent but there is a feeling behind-the-scenes that they could have the right man already in Solskjaer.
The board are believed to remain impressed with his knowledge of the market and what the squad needs to return them back to the pinnacle of the English game.
Solskjaer was instrumental in identifying and helping United to land all their targets during the summer, with one eye clearly towards the future.
Alongside £80m England defender Harry Maguire, Solskjaer showed expert handling to deliver right-back Aaron Wan-Bissaka and winger Daniel James from Crystal Palace and Swansea City respectively.
The one big question mark must be how the former striker would react to any new job offer, and whether he would prefer a clean break, with no blame attached to either side in an already uncomfortable situation.