Both sides are looking to secure an advantage ahead of the second leg at Nou Camp on April 16.
Barca are hunting a first Champions League title since 2015, while three-time winners Manchester United have not lifted Europe’s biggest prize since 2008.
The Catalan giants sit 11 points clear in La Liga and are closing in on a second consecutive title after beating second-placed Atletico Madrid on Saturday.
Having topped their group featuring PSV, Inter Milan and Tottenham, Barca then saw off Lyon 5-1 in the round of 16.
Their opponents on Wednesday were second in Group H behind Juventus, with Valencia and Young Boys eliminated.
After losing 2-0 at home to Paris Saint-Germain in the round of 16 first leg, boss Ole Gunnar Solskjaer masterminded a memorable comeback to set up the quarter-final clash.