The former director of football for the German national team believes Klopp has the qualities to lead the country, but also warned that Germany no longer possesses the depth of outstanding players it once had.
“We have one, two, three, four very good players. But overall we no longer have as many very good players as we did before,” Bierhoff said during a media round.
Bierhoff was much more positive when assessing Klopp, who recently took charge of the national team.
“Jürgen Klopp is a great coach. He has energy, charisma and experience.”
The former Germany official has previously criticised the way the country handled its recent coaches, arguing that Joachim Löw, Hansi Flick and Julian Nagelsmann were all successful and competent managers who were ultimately worn down by the national-team environment.
Klopp's early decisions are already attracting scrutiny, particularly his handling of Bayern Munich goalkeeper Jonas Urbig.
The 23-year-old is viewed as Bayern's future No.1 and has now been given the opportunity to make his first international appearances. Klopp, however, has explained the decision in terms of the goalkeeper's lack of regular club football.
“All the boys we have with us play regularly. Jonas is different. That's why we planned for him to get another game.”
Urbig is expected to start against Greece, despite having made only two appearances for Bayern this season.
Klopp acknowledged that using international matches to provide club playing time is unusual, but offered a light-hearted explanation.
“Normally, international players get match practice at their clubs. With us it is different. With us there is all inclusive.”
The decision nevertheless raises questions about the principle behind national-team selection. Goalkeepers who have been playing regularly for their clubs could reasonably feel overlooked when Urbig is selected partly to compensate for his limited minutes at Bayern.
Klopp has not placed the same emphasis on the performance principle publicly as his predecessor Nagelsmann, but his treatment of Urbig demonstrates the different approach the new coach is prepared to take.
At the same time, Bierhoff's warning about Germany's declining depth provides an important backdrop to Klopp's first months in charge. The new coach has inherited a squad containing several outstanding players but fewer elite options than previous generations enjoyed.
His challenge will therefore involve both maximising the quality available to him and making difficult decisions over players who are not regularly playing at club level.
Bierhoff's endorsement gives Klopp an important vote of confidence, but the scrutiny over Urbig shows that his decisions will quickly be tested.