United have been in fine form since sacking Jose Mourinho a week before Christmas, when they were 11 points behind the top four.
Prior to last weekend, the Red Devils had found themselves back in a Champions League spot – but then Arsenal came along and beat them.
Before that defeat to the Gunners, the Old Trafford outfit had gone unbeaten in the league under Solskjaer – including a new away record.
They have also claimed the scalps of Arsenal and Chelsea in the FA Cup and managed an incredible result in the Champions League.
Despite losing 2-0 at Old Trafford, Solskjaer’s side managed to claw themselves back into the tie and are through to the next round.
On an incredible night at the Parc des Princes, United won 3-1 after goals from Romelu Lukaku and Marcus Rashford.
The Belgian striker scored a first-half brace with goals either side of Juan Bernat’s equaliser.
But in the dying embers of the game Rashford scored from the spot after a controversial decision from VAR.
Liverpool, on the other hand, blew away Bayern Munich in their own ground after a 3-1 victory to go through to the next round.
Sadio Mane scored a brace, his first a majestic chip that left Manuel Neuer dumbfounded, with Virgil van Dijk also scoring.
And former United boss Mourinho has taken a sly dig at his predecessor by claiming the Reds result trumps United’s.
He said: “I was looking at Liverpool, they were on their way down in the Premier League and they were losing lots of points.
“And they come with for sure the best performance of the season in the Champions League. For sure.
“So they managed to surprise me. I don’t think they surprised themselves because of course, they are the first ones to believe.
“But to surprise lots of people with that strong performance.
“That puts them now in of course a good position for the Champions League fight.
“But I think also by the mental point of view maybe they are reborn and they can bring this kind of performance to the Premier League.”