Family Minister Kristina Schröder has been pushing for a voluntary quota, while Labour Minister Ursula von der Leyen wants a legally enforceable one.
The two cabinet members are often depicted by the German media as being at odds.
The survey, published by Der Spiegel on Friday was commissioned by the ARD public television station. It showed one in four Germans favours legally requiring companies to hold a certain percentage of top manager jobs for women.
There was a big difference when it came to gender.
Nearly a third of the women questioned wanted a law requiring a quota, while just 17 percent of men shared that view.
The survey showed that 61 percent of people would like to see companies volunteering to ensure 30 percent of their management positions are filled by women, while 24 percent want that quota to be written into law.
The report was based on an ARD-German trend survey of 1,000 Germans conducted on Tuesday and Wednesday by the polling firm Infratest Dimap, the online site said.