United will host Lionel Messi and Co. in the opening leg of their quarter-final clash at Old Trafford on Wednesday evening.
Ole Gunnar Solskjaer's United – who completed a stunning comeback against Paris Saint-Germain in the last 16 – have lost three of their past four matches in all competitions and are still fighting to finish in the Premier League's top four.
When asked if beating Barca is possible, former United winger Olsen told Omnisport: "Of course it is. It's two games, isn't it?
"Barcelona have great experience, but I don't think that it's impossible but it's going to be very, very hard, of course.
"Anyone at this stage is going to be hard. I think really Man United is the underdog in this so they have more to win, and Barcelona more to lose."
United suffered a damaging 2-1 defeat away to Wolves last week. Solskjaer's side are currently sixth in the Premier League, three points adrift of fourth-placed Tottenham.
The Red Devils have six league matches remaining to secure a spot in next season's Champions League, but they can also qualify by winning the competition come May.
Barca head into the last eight tie in better form than their rivals, however, having won five of their last six matches.
A 2-0 win over Atletico Madrid at Camp Nou on Saturday saw Ernesto Valverde's men move ever closer to retaining the Spanish title and they are among the favourites to lift the European Cup once again next month.