"The Americans are acting just like they accuse the Chinese of acting," Trittin, co-chief of the Greens' parliamentary group, told ARD public television, referring to US accusations that Beijing sponsors state espionage of US interests.
He said Snowden, the former National Security Agency (NSA) contractor behind a series of damaging allegations about US spying, had "done Europe a service."
Snowden is holed up in a Moscow airport transit zone after the United States issued a warrant for his arrest and revoked his passport.
Trittin, a former environment minister, said it was "embarrassing" for western democracies that "such a person, who served the cause of democracy, who uncovered a major violation of fundamental rights, has to hunker down with despots who are at war with fundamental rights."
"I am of the opinion that such a person should be protected," he said, when asked whether Snowden should be granted asylum.
After the EU spying report in German weekly magazine Der Spiegel Berlin
said the United States must quickly say whether the allegations were true.
The German opposition has leapt on the issue three months before a national election, demanding Chancellor Angela Merkel take a tough line with Washington.
Merkel's spokesman Steffen Seibert expressed shock Monday over the reports of US spying on European institutions and said it had told Washington that it must restore trust in the wake of the allegations.
He said he was not aware of any attempt by Snowden to seek asylum in the EU and said any application would be reviewed on the basis of the Geneva Conventions.
"They apply to everyone," Seibert said.