Schulz, a German Social Democrat, told public broadcaster ARD that Snowden, who has reportedly submitted asylum requests to 21 nations, had helped the global cause of transparency by exposing the alleged US bugging.
"I believe Mr Snowden showed us that the United States of America treats its closest partners including Germany, for example, but also the European Union as a whole like hostile powers," he said.
"That is absolutely unacceptable. That is why the authorities will have to determine when Mr Snowden submits an application whether he is actually being politically persecuted.
"But I am sympathetic to this application," he said, when asked whether Germany should take him in.
WikiLeaks said Monday that Snowden had submitted asylum requests to countries including Cuba, Venezuela, Brazil, India, China, Russia, Germany and France, in addition to earlier requests to Ecuador and Iceland.
However, a Kremlin spokesman said Tuesday that Snowden, who is in legal limbo in the transit zone of a Moscow airport, had abandoned his request for political asylum in Russia after it told him he would have to stop leaking US intelligence reports.
Schulz said Europeans were "deeply disappointed" in US President Barack Obama in light of the allegations, adding that security justifications for the eavesdropping appeared bogus.
"I cannot imagine that at institutions such as the EU embassy in Washington there were terrorist acts being planned and that's why microphones were installed," he said, referring to one of the supposed targets of the alleged US spying exposed by German news weekly Der Spiegel using documents provided by Snowden.
"These are methods that were used earlier by the KGB, " he said referring to the former Soviet secret services during the Cold War.