Jurgen Klopp's announcement he would step down as Liverpool manager at the end of the season was greeted with shock in his native Germany on Friday, leading to speculation he could be set for a move to the national side.
Klopp said he would leave the Premier League club he has coached since 2015 at season's end because he was "running out of energy".
"I just heard the news a couple of minutes ago, it's really shocking," said Bayern Munich manager Thomas Tuchel.
Tuchel, who succeeded Klopp at Mainz and later Borussia Dortmund, called the Liverpool boss "one of the very best coaches in the world".
"Wherever he was, he always managed to put a stamp on the clubs that he was with."
Klopp has long been considered a candidate to take over the national team, particularly amid Germany's struggles in recent years.
Current national coach Julian Nagelsmann's contract runs out after Euro 2024, the same time Klopp indicated he will finish up at the Reds.
The German FA (DFB) did not comment when asked by AFP sports subsidiary SID on Friday, but are known to be long-term admirers of the 56-year-old.
Klopp's former club Dortmund, where he won two Bundesliga league titles and took the club to the 2013 Champions League final, also reacted with surprise.
Dortmund CEO Hans-Joachim Watzke, who was responsible for recruiting Klopp, telling SID the timing and manner of the announcement "shows once again that Jurgen is exceptional".
"I have great respect for this decision."
Dortmund manager Edin Terzic, who was an assistant junior coach during Klopp's tenure and still stays in regular contact with him, said the news "came as a surprise to me".
"Thankfully I know Jurgen pretty well and I know that no matter what decisions he has made in his life so far, he has thought them through very carefully and that is why I am sure that this decision feels like the right one for him.
"He is an oustanding person, an incredible coach and I was very lucky to watch him up close and get to know him.
"He has shaped our club like no other over the past few years and he did exactly the same at Liverpool."