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Bayern removed Nagelsmann from his post despite club officials recently describing him as a "long-term project", replacing him with former Borussia Dortmund, Paris Saint-Germain and Chelsea coach Thomas Tuchel on Saturday (AEDT).
Many of Bayern's players are away on international duty this week, and Kimmich – among its most senior stars – appeared in Germany's pre-match press conference on Friday ahead of a friendly against Peru.
While unwilling to openly discuss what at the time as a rumour about Nagelsmann, he was unequivocal in his regard for the now former Bayern coach.
"It's generally understandable that it's a hot topic, but there was no confirmation from the club, so I ask for your understanding that I won't say much more about it," he said.
"Of course, such talk concerns you [as a Bayern player]. It's about the coaching position in your own club, he's the coach you work with every day.
"But that shouldn't play a role in [Saturday]'s game or in training here."
He added: "Julian Nagelsmann is an outstanding coach.
"I've had a lot of top coaches now, but I'd say he's easily in the top three of my previous coaches. But I can't say anything about the current state of affairs."
The situation appears to have come out of the blue given Bayern won the Bundesliga last season, is firmly in the title race this term, and remains in contention in the UEFA Champions League.
However, the club's hierarchy was unimpressed by the team's form since the turn of the year, dropping 12 points in 10 Bundesliga games.
That has contributed to it falling a point behind rival Dortmund, its next opponent in Der Klassiker on 2 April (AEDT).
Incoming Tuchel has been out of work since September 2022 but was being strongly linked with Tottenham Hotspur, which is expected to part ways with Antonio Conte, and a second stint at PSG, where Christophe Galtier's future is uncertain after the UEFA Champions League elimination of which Nagelsmann was the architect.
Nagelsmann's predecessor at Bayern was Hansi Flick, the current Germany head coach. Flick did not hide his shock at the situation, but was eager to ensure it did not become a distraction.
"We were very, very surprised by the headlines last night, but I don't think Bayern Munich has commented on that yet," Flick said.
"Out of respect for Julian and Bayern, I won't say anything on the subject during the press conference. That says it all."
He added: "It's not going to impact everyone. Still, it's my job to talk to all the players – I've already done that. Now we have to wait and see what really comes out in the end."
