Former Liverpool, Fulham and Crystal Palace manager Hodgson took charge of Bristol City last week at the age of 78.
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A stunned Klopp told BBC Sport: "Is it true that Roy Hodgson is the new manager of Bristol City? And he turns 79 in August? Roy.
"I asked you last time if your flat is wet or whatever, but it's really crazy. Good luck."
Klopp also stated: "But they are 12 points ahead of the relegation zone, right? Then it's not the most difficult job at least, Roy! Enjoy, in Bristol, the good times.
"For some it's forever, let me say it like that."