Quoting "investigating sources", Welt am Sonntag said that a "substantial consideration" was made to secure his release.
But the newspaper quoted the foreign ministry as insisting that no ransom was paid for the man's release.
Contacted by AFP, the foreign ministry refused to make any comment on the report.
The man, whose name has not been released, is from the eastern state of Brandenburg and had travelled to Syria in June 2013 with the intention of offering "humanitarian aid".
His family reported him missing when he failed to contact them, the newspaper said.
Then earlier this year, the man's family received a video containing a ransom demand and also showing the execution of another hostage, the newspaper said.
The German authorities – including the federal police BKA, the BND intelligence services and the foreign ministry – subsequently entered into negotiations with the kidnappers.