The Suddeutsche Zeitung (SZ) daily and regional public broadcasters NDR and WDR said documents passed to the CIA by one of its moles inside German intelligence show it eavesdropped on Clinton while she was on a US government plane.
But a German government source told the three outlets that the intercept happened by accident, and only once.
Berlin and Washington have been at loggerheads over alleged US snooping, with the head of the CIA in Germany expelled last month as revelations of double agents and the bugging of Chancellor Angela Merkel's mobile phone soured relations between the allies.
The reports did not reveal when the eavesdropped Clinton conversation took place, but they said John Kerry, her successor as the top US diplomat, may have brought the matter up with his German opposite nunber, Frank-Walter Steinmeier.
According to the reports, the Clinton intercept was "not an isolated case", with the German government apparently giving permission for "spying on a NATO partner", although it was unclear which of its allies was the target.