Muller is considering his future at Bayern, where the 30-year-old forward has not started a league match under Niko Kovac since September's draw against rivals Leipzig.
A January exit has been touted for Bayern veteran Muller, who was linked with a move to Premier League giants Manchester United previously.
Asked about Muller following Germany's 2-2 international friendly draw with Argentina on Wednesday, Kimmich told reporters the club would struggle to replace such an iconic figure but can see where the veteran attacker is coming from.
"In the first place a very big identification figure would leave the club, especially for the fans," Kimmich said.
"I myself know the Bayern only with Thomas Muller. Without him the club would not be there, where it is now. It's the case that when he comes into the game he always plays well. In the last game he has set up another goal. Also in the games before.
"Against Cologne or Mainz he even assisted two goals and also scored one goal, if I remember right. We all know that he has qualities that are difficult for the opponent to control.
"I don't know if he wants to go or not. I can understand that he claims to want to play. I know what it's like to sit on a bench.
"With [former head coach] Carlo Ancelotti I also sat on the bench several times. It's completely normal for a player to be dissatisfied or become dissatisfied."
Muller emerged from Bayern's youth system in 2008, and he has since won eight Bundesliga titles with the Bavarian powerhouse.
He has also celebrated Champions League, UEFA Super Cup, FIFA Club World Cup, DFB-Pokal and DFL-Supercup titles during his time in Munich.
Across his seven league appearances this season, Muller is yet to score but has contributed an impressive four assists despite being used primarily as a substitute.
Last season, the German attacker was a first-team regular and managed just nine goals across all competitions.