Two Norwegian politicians nominated Snowden, saying his actions have contributed to making the world more peaceful.
"We do not necessarily condone or support all of his disclosures," the two lawmakers said in their nomination letter. "We are, however, convinced that the public debate and changes in policy that have followed in the wake of Snowden's whistleblowing has contributed to a more stable and peaceful world order."
Snowden has been living in Russia under asylum after fleeing the U.S. He is wanted in the United States on charges related to the leaks.
Anyone can be nominated for the Nobel Peace Prize, which usually goes to members of government, university professors or previous laureates. Nobel Committee members can add their own candidates at their first meeting after Saturday's deadline. The winner will be announced in October. The Organization for the Prohibition of Chemical Weapons won last year's Nobel Peace Prize.
Also on Wednesday, Director of National Intelligence James Clapper told a Senate Intelligence Committee hearing that he wants Snowden to return the rest of the secret documents he took before making them public.
Clapper said Snowden's disclosures of National Security Agency spying have caused "profound damage" by revealing surveillance methods to terrorists, who he says are changing how the communicate to avoid detection.
Snowden took a trove of documents about the NSA's surveillance programs, revealing that the agency sweeps up millions of Americans' phone and Internet records. The ensuing outcry has led President Barack Obama to ask agencies and Congress to consider some reforms.
The Associated Press contributed to this report.