We will play the first leg at home on Tuesday 9 April, kick-off 8pm, with the second leg to be played away on Wednesday 17 April, kick-off 8pm.
Klopp's Liverpool are fighting for Premier League and Champions League silverware after splashing the cash on Alisson, Fabinho, Naby Keita and Xherdan Shaqiri in the off-season.
Twenty years on, he will be back in Barcelona for the second leg of the quarterfinal tie as Red Devils coach.
Home teams dominated again in Week 30, winning seven of the 10 matches. Jürgen Klopp will be confident after the Champions League victory over Bayern Munich.
The Reds have won each of the last five meetings with the Cottagers across all competitions - a new club record run versus the London side. "It's not by accident that three German clubs are eliminated by three English clubs".
Following on from the Champions League draw, both Arsenal and Chelsea have found out which teams they would face in the quarter-finals of the Europa League.
The winners of Spurs vs. Man City will host either Ajax or Juventus in the first leg of the other semi.
Ajax, once a major European power who struggle to compete financially with clubs from bigger leagues, ousted Real in the last 16 and their tie against Juventus will be a repeat of the 1996 final, which the Serie A club won on penalties.
Expectations are high that Guardiola, who twice guided Barcelona to Europe's top prize, will lead the Premier League champions into the final four for the first time since taking charge in 2016.
Last year, Cristiano Ronaldo was bought by Juventus, a team which has lost two finals in the past four years, to end that 23-year wait.