I’ve never found a reliable source for this, and I’m pretty sure it’s not a Goethe quote. Most telling is that I’ve never seen a German or Greek/German version of it. Moreover, it doesn’t sound particularly like Goethe.
There are a lot of quotes unduly attributed to Goethe — another sign of his prominence. Somewhat surprising is that many are originally in English. I recall finding out a few years ago the source of another one, which turned out to be a Scottish author (I think it was something about following your dreams).
However, for a real quote : He may have been the first respectable writer to put into print “Er kann mich im Arsch lecken!”
Goethe’s influence on the German language can be likened to Shakespeare’s.
(on English, that is.)