Magazine Der Spiegel published the story amid mounting fears that Europe's largest economy could slide into a recession. The Finance Ministry declined to comment on Spiegel's report.
The small selloff in German and other euro zone government bonds late on Friday came after another strong rally this week, which has seen German and other countries' borrowing costs repeatedly plumb new lows as investors unnerved by talk of a recession piled into safer assets.
The German 10-year bond yield was last up more than four basis points at -0.658%, having earlier hit a record low of -0.727% on heightened expectations for aggressive European Central Bank easing soon. Yields on the five and 30-year bonds also rose.
Other euro zone bonds, including those in Italy and France were also higher.
While many expect bond yields to remain at ultra-low levels, Friday's jump underlines investors' sensitivity to any sign of fiscal expansion after the huge rally in bonds in the last few months has accelerated since the start of August.
Some also believe market concerns about recession risks are overdone.
"We don't see a recession coming 'imminently' even though the US yield curve has inverted," said Fahad Kamal, chief market strategist at Kleinwort Hambros. "Bonds remain hideously expensive."
Ten-year bond yields in Germany were set for a fifth straight week of declines, Italy's 10-year bond yield was poised for its biggest weekly falls since mid-2018 and Spanish 10-year yields, down 23 basis points this week, were on track for their biggest weekly fall of 2019.
Yields had earlier hit new record lows across the euro zone after ECB policymaker Olli Rehn on Thursday flagged the need for a significant easing package in September.
Alongside increasing concern about global recession risks, fuelled after the US bond yield curve on Wednesday inverted for the first time in 12 years, this has meant another stellar week for bond markets where prices have shot up - pushing yields down.
"The underlying concern and drivers such as a recession and the expectation for an aggressive policy response, fuelled by Rehn's comments yesterday, has given the bond market another boost at already elevated levels," said Commerzbank rates strategist Rainer Guntermann. In a sign of relentless demand for yield, Germany 30-year yields touched a fresh record low of -0.313% earlier on Friday.