The Red Devils will host the Spanish title holders in the first leg of their Champions League quarter-final at Old Trafford on 10 April.
Manchester United will have to contain one of the world’s greatest players, Lionel Messi, if the Red Devils hope to have any chance of reaching the last four.
Solskjaer’s side sprung a surprise in the previous round having lost 2-0 to Paris Saint-Germain in the first leg at Old Trafford.
Manchester United rallied in the French capital as goals from Marcus Rashford and Romelu Lukaku sealed a 3-1 win at the Parc des Princes to secure their progress.
The Red Devils haven’t reached the Champions League semi-finals since Sir Alex Ferguson’s retirement.
Wales manager Giggs believes FC Barcelona will be worried about Manchester United despite starting the last-eight clash as favourites.
“It’s tough – I think most people wanted to stay away from Barcelona [in the draw],” Giggs told Man United’s website.
“Ole, especially, has got good memories of the Nou Camp. I don’t know whether he’ll put himself on the bench that night. He might have to think about that!
“After beating PSG in the manner we did, with the spirit and character showed, I don’t think anybody will be looking forward to facing us either.”
Solskjaer scored the winning goal in a 2-1 victory over Bayern Munich in the Champions League final at Camp Nou in 1999.
The Red Devils have lost successive games for the first time under Solskjaer after Arsenal were 2-0 winners against Manchester United before Wolves beat Solskjaer’s side in the FA Cup quarter-finals.
Manchester United haven’t won the Champions League since 2008.
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