PSG outplayed United 2-0 at Old Trafford last month to take complete control of their last-16 tie and Solskjaer's side will be without inspirational midfielder Paul Pogba due to suspension.
Anthony Martial is a major doubt and midfielders Ander Herrera and Nemanja Matic are also both expected to miss the trip to the French capital due to injury.
United's hopes of a Champions League comeback appear slim but Solskjaer, who scored an injury-time winner against Bayern Munich to seal their dramatic success in the 1999 final, is backing his side.
"We can't write games off, we've been fantastic away from home," Solskjaer told United's official website. "We're not going to go out without giving a fight.
"We're going to go out there and enjoy the game. We know it's a difficult place to come and they played really well at Old Trafford, so it's a great challenge for our players to go out there and show what they can do.
"We'd rather win 4-2 than try to get a 2-0. We've got to get to half-time better off than we are now. If you can get to 1-0 at half-time then anything can happen in the second half.
"Against PSG, in the last 20 minutes, I know they were 2-0 up so they were happy, but I thought we held our own and Victor [Lindelof] back there marshalled the troops, so we can go there and score a goal and make it chaotic in the last 15 or 20 minutes.
"He's a big, big plus. His performances have risen and really improved. He's playing more on the left side; he started really well on the right side with Phil Jones, now Chris Smalling has come in and done really well, so he's has loads of partners to play with. I think he's easy to play with for the other centre-backs because he's so reliable."
United have won all eight of their matches away from home in all competitions since Solskjaer was installed as the temporary replacement for Jose Mourinho.
"It's an incredible achievement by the players," Solskjaer added. "They go into away games now knowing that we can defend well and we've got pace on the counter.
"They've been very confident away from home so hopefully we can take that to Paris because we have to - we're playing against top, top players."