Klopp announced earlier this month that he will leave Signal Iduna Park at the end of the 2014-15 campaign.
In his seven seasons in charge of Dortmund, Klopp won two Bundesliga titles, one DFB-Pokal and led the club to the final of the 2012-13 Champions League, which they lost to Bayern.
Dortmund will travel to Bayern on Tuesday with a spot in the cup final on the line and Kagawa wants to send the 47-year-old coach out on a high after a tough season in which they have been forced to battle against the threat of relegation.
"We feel a great sense of gratitude and we owe him," Kagawa told the Bundesliga's website.
"Soon it'll be time for him to go and that won't be easy, which is all the more reason why it's now about us giving even more for the coach in the last few games."
Dortmund arrive in Munich with four wins in their past six matches in all competitions, plus a 1-0 loss to Bayern at home at the start of April.
In their past two games, BVB have not conceded a goal as they beat Paderborn 3-0 and Eintracht Frankfurt 2-0, with Kagawa scoring in both Bundesliga fixtures.
"The Bayern game's coming at a good time for us. We'll be able to take our momentum from the league into the semi-finals of the cup," the Japan international said.
"The last few games have given us a lot of belief. That's what we want to draw on in the cup and show in Munich on Tuesday."