Liverpool claimed a 2-0 win over the Italian champions in the first leg at the San Siro three weeks ago, with Roberto Firmino and Mohamed Salah getting on the score sheet.
Despite hailing Liverpool's advantage from the first leg, Klopp is guiding against complacency when the Nerazzurri come to town.
"It's a danger everyone knows about: it's a lead that gets turned over the most in the history of football I think," Klopp told reporters.
"You can't have a team at half-time that thinks they are already through. Then you are on the wrong path.
"It's a much better result than we expected if I'm honest. The game didn't look like we would win it 2-0 for most of it. It is a tough tie and was a really difficult game.
"We knew they had quality but now we know they have real quality. They will show up here after winning their last game 5-0. Yes, against bottom of the table, but still really impressive. [Lautaro] Martinez scored [a hat-trick], [Edin] Dzeko scored, [Robin] Gosens is back.
"I'm really happy [Nicolo] Barella isn't playing because he set up three or four chances. That's a really good, experienced team who don't come here as tourists.
"They want to chase the game and that's what we want to do, we're not a team that defends results. We want to attack the game, so let's see what we can do."
Having already secured the Carabao Cup, Liverpool are still in the hunt for three more trophies to complete a famous quadruple.
