In an interview with Spiegel published on Friday, Gauck - who will be replaced by Frank-Walter Steinmeier this month - voiced his concerns about the Republican President.
“It worries me a lot that the American President is putting some things into questions that generations of other Americans have achieved with Europeans,” said Gauck.
The German President further condemned Trump's fraught relationship with the media as he has referred to many major news outlets as “the enemy of the American people”.
“This damages democracy,” Gauck said.
He also said that the “many law-abiding US citizens will not forget” how Trump has rallied against his other perceived opponents, such as a federal judge who blocked the President's controversial travel ban.
The German leader further said that while the United States used to be a “place people longed for” and a “role model”, it currently is not such things.
Trump's administration has come in for criticism from a number of German politicians - except those from the far-right Alternative for Germany (AfD), whose members sometimes cite him as inspiration.
Before Trump was elected, Gauck said he was worried about the country electing the “unpredictable” real estate mogul.
Gauck's successor, former Foreign Minister Steinmeier, has been called the ‘anti-Trump' for his outspoken criticism of the American leader.