The Premier League rivals will meet for the first time in European competition as they face off for a place in the quarter-finals over two legs.
Klopp's only previous encounter with United as Liverpool boss ended in a 1-0 home defeat last month, but the German is relishing the opportunity to put things right.
"It's great," he told a news conference. "We deserve these games. It's not easy. I told my staff yesterday that I wanted Manchester United.
READ MORE | Carragher hits back at Diouf
"We had a good game [in January] and lost 1-0. It was not what we deserved.
"It gives us the chance to make it better. In this round, there are no easy games. Manchester United? Good."
Goalkeeper Simon Mignolet, who revealed some players were still training when they discovered the result of the draw, added: "It's a fixture to look forward to.
"You want to get drawn against European teams but we have a derby. Two big games."