The figure will be formally announced on Wednesday when Finance Minister Olaf Scholz presents next year's federal budget.
Berlin already intends to borrow around €218 billion this year to help pay for massive stimulus and rescue measures aimed at steering Europe's top economy through the Covid-19 crisis.
A Finance Ministry source told news agency DPA: “Doing nothing would be much more expensive.”
The unprecedented spending has forced Chancellor Angela Merkel's government to abandon its years-long habit of running a “black zero” balanced budget, and suspend a constitutionally enshrined “debt brake”.
Introduced at the height of the financial crisis in 2009, the “debt brake” bans Berlin from taking on more than 0.35 percent of gross domestic product (GDP) in new debt in any one year.
Scholz's 2021 budget would see total government debt as a percentage of GDP climb to 75.25 percent, compared with just under 60 percent in 2019.
Germany expects to return to the “debt brake” and its usual fiscal rigour in 2022, the ministry sources said.
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The government is also bracing for a massive drop in tax revenues this year and next.
The country now expects to take in €264.4 billion in federal tax revenues in 2020, down from Scholz's earlier prediction of €275 billion, and well below the €329 billion collected in 2019.
Tax revenues are not expected to reach their pre-crisis level until 2024, the sources said.
Support for people and businesses
Merkel's ruling coalition has pledged more than a trillion euros in aid to shield German companies and workers from the virus fallout, including through loans, grants and subsidised shorter-hours programmes.
The government has also rolled out a €130-billion stimulus programme to kickstart the economic recovery, including major investments in the health sector.
The German economy is predicted to contract by 5.8 percent in 2020, the deepest slump in its post-war history, before rebounding by 4.4 percent in 2021.