Goals from Presnel Kimpembe and Kylian Mbappe secured victory for the Ligue 1 champions at Old Trafford last month and left United needing to produce something remarkable in the French capital in order to turn the tie around.
None of the previous 34 teams to lose the first leg of a Champions League knockout match at home by two or more goals have ever progressed to the next round.
To make things even tougher, the Red Devils are without the suspended Paul Pogba and a string of first-team players due to injury, with Anthony Martial, Jesse Lingard, Ander Herrera, Juan Mata, Nemanja Matic and Alexis Sanchez are all absent.
As a result Solskjaer has included a number of youngsters in his travelling party, including 17-year-olds Mason Greenwood and James Garner.
However, the United interim boss is refusing to be downbeat and still believes his side are capable of mounting a dramatic comeback.
"Never... never mission impossible,” the Norwegian told reporters. “It is a difficult test, but we can do it. We need the first goal and we need to stay in the game. Anything can happen. We need a good plan.
“Everyone knows we can do it, we’ve done it. Last year Juventus lost 3-0 to Real Madrid and then went 3-0 up in second-leg, PSG vs Barcelona [in 2017]. There are so many examples of teams who can change results like this.
“When no one believes in you, there’s always that bit of character you have to show. These players are not used to losing and we’re not happy with the loss in the home leg.
"Making history is not the motivation, qualifying is. At our best, we can match them. We have to get the first goal and then anything can happen. Goals always change games and if we get the first one we will start believing.”
Reflecting on the first leg, Solskjaer says it was a harsh reminder as to the ruthlessness of the Champions League.
“I was disappointed, not unhappy,” added Solskjaer. “At half time 0-0 with the injuries we had we spoke about keeping a clean sheet because that was vital. I was disappointed with the way we conceded.
“We analyse games but in the heat of the moment we made a couple of mistakes and when you make small mistakes you get punished.
“You can get away with it in the Premier League but can’t in the latter stages of the Champions League.”