Only one in three participants in the Deutschlandtrend opinion poll for public broadcaster ARD by Infratest Dimap said von der Leyen would be a good choice for the top EU position, while 56% rejected this viewpoint.
The poll regularly looks into a wide range of political and social issues.
In the latest poll, 54% of Germans were found to have been very satisfied or somewhat satisfied with the performance of Angela Merkel as chancellor. However, only 29% were content with the performance of her government.
Germany's Greens managed to stay the country's most popular political party, garnering 26% support. This put them a point above the CDU/CSU conservative bloc. The moderate left SPD remained neck-and-neck with the populist AfD, with both parties scoring 13% in the survey. The race between the business-friendly FDP and left-wing Linke was equally tense, with both of the parties polling at 8%.
More fear from right-wing violence than Islamist attacks
Outside party rivalries, the survey found that 66% of participants believed that the state was too often giving Nazis and far-right extremists a blank check. Some 67% were worried that far-right extremists could "change" the state, and 71% believed there was a significant danger of far-right attacks.
In comparison, only 60% believed there was a serious danger of Islamist attacks.
Also, nearly two-thirds (65%) were in favor of giving security services more authority to monitor online communication and social media.
Pressure mounts on Italy
Deutschlandtrend also surveyed Germany's attitudes on saving migrants at sea, with 72% of participants expressing their support for charities that save refugees and the same percentage saying that saving migrants should not be persecuted.
Last week, Italy detained German captain Carola Rackete after she steered a rescue ship with dozens of migrants into a port without authorization from the Italian government, ramming a patrol boat in the process. Rackete's move prompted a discussion in Germany and Europe about charities operating in the Mediterranean Sea.