The Rossoneri are on a 13-game unbeaten run in all competitions but still go into the pivotal showdown seven points behind their city rivals, who sit fourth in the table.
While Inter have struggled of late - winning just twice in their last 11 Serie A outings to dramatically fall out of the title race - Gattuso has warned his players not to get too complacent.
"If we want to think of a Champions League place, then this is like a final," he told the media.
"The thing I fear the most is the history of the derby, as usually the team that is struggling tends to win. I don't like people saying we are the favourites.
"Coach [Luciano] Spalletti scares me because he is a great manager. He has a lot of experience and is very prepared, so he knows how to face these types of matches.
"We have to be cautious. I fear the idea some could think we're suddenly fantastic and forget where we started from. We've done nothing yet and still need to become a team.
"We've got the potential to do great things, but must not lose that sacrifice for hard work. I will keep smashing them with that, even if they glare at me and can't stand it anymore, I will continue hammering at that nail.
"As long as my players show respect – not for me, but for the locker room, their team-mates and the club – I will tear my heart out of my chest and let them play keepy-uppy with it."
Spalletti has confirmed Inter talisman Mauro Icardi is "more than ready" to face Milan, despite not starting a game since January 28 due to a knee injury.
"Am I worried about Icardi? Absolutely," Gattuso replied when asked about the Argentine striker.
"He is one of the best strikers in the world. He moves in an incredible way, only a few are better than him. He never misses, he is a sniper. We must pay attention to [Antonio] Candreva and [Ivan] Perisic as well."