Someone else has traced the quotation to a novel by Upton Sinclair in The Profits of Religion (do a books.google.com search for the phrase and you will find it.
In short, it is highly unlikely that Goebbels said this. As is usually the case with such quotations, no one who cites it provides a source.
Randall Bytwerk, expert in Nazi propaganda (Prof. Randall Bytwerk)
The origin of the quote is not Goebbels.
https://skeptics.stackexchange.com/questions/30683/is-if-you-have-nothing-to-hide-you-have-nothing-to-fear-a-line-used-by-joseph#40126