Greenwald was the first journalist to whom Snowden leaked documents to last year about the National Security Agency’s surveillance programs.
In an interview with Israel’s Channel 10 TV on Monday, Greenwald was asked if the former NSA contractor has more documents about Israel, reports say.
"Yes. I don't want to preview any stories that aren't yet published, but it is definitely the case that there are a huge number of very significant stories that are left to report," Greenwald said, speaking from Brazil, where he lives.
In late December, Germany magazine Der Spiegel reported U.S. intelligence worked with their British counterparts in 2009 to monitor the communications of Israel’s former Prime Minister Ehud Olmert and former Defense Minister Ehud Barak.
Since June, Snowden’s leaks have revealed the NSA has spied on other foreign governments’ leaders and their citizens. Greenwald suggested Snowden would leak more documents.
"We have only had these documents for seven months, which, given their volume and complexity, is not a very long time. There definitely are stories left that involve the Middle East, that involve Israel. The reporting is going to continue at roughly the same pace that has been happening."
Snowden faces espionage charges in the U.S. The New York Times called for the Obama administration to grant Snowden clemency last week. The White House has previously downplayed that idea.