The former Germany defender cited Klopp as the outstanding candidate to take over the Bavarian giants.
Having parted company with Carlo Ancelotti, Bayern are in the market for their next boss, and currently trail table-topping Borussia Dortmund by five points in the Bundesliga.
Metzelder told Sky Sports Germany: ‘From my point of view, Jurgen Klopp would be ready.
‘He is a top man-manager and could make the complex power relationship work wonderfully.’
Klopp took charge of the Reds in 2015 and has spoken of his desire to be at Anfield for the long haul as he establishes his project at the club.
But Metzelder thinks the 50-year-old is the leading candidate to take charge at Bayern, with Willy Sagnol having assumed control on an interim basis.
Former Dortmund manager Thomas Tuchel and up-and-coming young Hoffenheim boss Julian Nagelsmann are also being discussed.
Metzelder has been impressed with the latter, but thinks such a massive club could be a step too far in the career of the 30-year-old.
‘[Julian] Nagelsmann is an outstanding trainer, but Bayern Munich is of course a different size [club to Hoffenheim],’ he added.
It would be a surprise if Klopp decided to depart Liverpool and he is likely to prioritise his side’s recent shortcomings ahead of speculation regarding his future.