The classified document, dated April 2013, states that the US secret services are especially interested in gathering intelligence concerning the 28-member bloc's foreign policy, international trade, and economic stability, the magazine reported.
Using a ranking system from one to five (from high to low importance), those three areas were given a number three ranking, according to the document seen by Der Spiegel. Topics related to new technology and energy security were assigned the lowest-level priority.
Among individual countries, Washington reportedly listed China, Russia, Iran, Pakistan and North Korea among its top surveillance targets.
Germany, France and Japan were considered of mid-level interest, the weekly
The latest revelations appear to back up earlier NSA documents released by Snowden that claimed that Washington was snooping on EU offices in Brussels
and in the States, sparking outrage among European countries, Der Spiegel said.
Snowden's leaks in recent weeks, which have revealed that the US is systematically seizing vast amounts of telephone and online data around the world, have proved a major headache for Washington and even threatened to derail a huge US-EU trade deal.
US President Barack Obama has scrambled to reassure allies and American citizens about the extent of the spying.
On Friday he pledged to overhaul US secret surveillance, promising greater oversight and transparency.
Snowden, who is wanted by the US on espionage charges, was granted temporary asylum in Russia earlier this month, a move that so angered Obama that he cancelled an upcoming high-profile meeting with President Vladimir Putin.