The Enhedslisten party submitted the name of the former U.S. National Security Agency contractor because his revelations had stirred an intensive public debate about government surveillance, the Copenhagen Post reported.
Party spokesperson Stine Brix announced the nomination on Twitter.
"The Internet, email and text messages make possible a surveillance society that is even wilder than George Orwell's book '1984', or what was seen in East Germany, but that is on its way to becoming a reality," Brix told a Danish newspaper.
Another Danish MP, Uffe Elbaek, had called for Denmark to grant Snowden asylum shortly before he was given asylum in Russia.
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