With Britain set to vote in an in-out referendum on June 23rd, the question is particularly pressing in the latest monthly Deutschlandtrend poll for public broadcaster ARD.
Just 15 percent of people said that they thought Britain should leave the EU when voters there go to the polls later this month.
That's despite the fact that most people thought Brexit would have no negative impact on the EU economy.
Half of respondents thought there would be no economic blow for Europe if Britain were to leave, while three percent thought things would even get better.
Thirty-nine percent said things would be worse if the UK quit.
The public's views echo those of Chancellor Angela Merkel, who on Thursday said that Britain was a valuable ally for Germany inside the EU and that she hoped the British would vote to keep their seat at the Brussels table.
Tough on Turkey
Three-quarters of those polled – 74 percent – said that it would be right for German MPs to declare the massacres of Armenians by the Ottoman Empire during the First World War a genocide in a vote on Thursday, although the poll took place before the parliament voted on the matter.
The Bundestag (German parliament) voted almost unanimously on Thursday in favour of calling the systemic murder of an estimated 1.5 million Armenians a genocide.
Holding a vote was widely seen as a risky move given Germany and Europe's dependence on Turkey to halt the flow of refugees coming from Syria and other conflict zones in the Middle East and further afield.
Turkish President Recep Tayyip Erdogan. File photo: DPA
When MPs voted the resolution through, it so angered Ankara that the Turkish ambassador to Berlin was recalled.
But there has been no sign thus far that the refugee agreement is under threat.
Germans want the government to get tougher with Turkey, with 89 percent in Friday's poll saying the federal government and the EU should offer President Recep Tayyip Erdogan no concessions, such as visa-free travel for his citizens, until he's fulfilled EU preconditions including toughening anti-terror laws.
New low for government parties
Meanwhile there was evidence of further loss of trust for Merkel's Christian Democratic Union (CDU), who lost one percentage point of support compared with last month's poll.
Chancellor Angela Merkel File photo: DPA
Just 32 percent of people would vote for the CDU if there were an election on Sunday – almost 10 percent short of the 41.5 percent vote share they and their Bavarian allies the Christian Social Union (CSU) won in 2013 parliamentary elections.
Both their coalition allies the Social Democratic Party (SPD) and the Left party gained one point – although the SPD remains far short of historic levels of support at 21 percent.
Merkel remains the most popular candidate for Chancellor, with 46 percent saying they'd choose her while just 23 percent named SPD leader and current Vice-Chancellor Sigmar Gabriel.
But almost a third of people – 28 percent – said that neither of the two was right for the job.
Pollsters surveyed 1,006 people on May 30th and 31st about Brexit and Turkey, and 1,506 people between May 30th and June 1st about political questions.