The axe fell one day after the German outfit suffered a 3-0 loss to Paris Saint-Germain in the Champions League last week.
Klopp, who has been in charge of Liverpool since October 2015, has been linked to the vacancy at the Allianz Arena, and Metzelder thinks that the 50-year-old is good enough to lead Bayern.
"From my point of view, Jurgen Klopp would be ready," the retired footballer told Sky Germany. "He is a top man-manager and could make the complex power relationship work wonderfully."
Klopp won five trophies during his seven-year spell in charge of Borussia Dortmund.