Authorities have so far predicted that Europe's top economy would record between 800,000 and one million new arrivals in 2015.
But Bild quoted the document saying that the authorities were now expecting to receive 920,000 new arrivals in the coming three months alone, bringing the total number of asylum-seekers this year to 1.5 million.
"The migratory pressure will increase. For the fourth quarter, we expect between 7,000 and 10,000 illegal entries a day," according to extracts of the document, although Bild did not specify its source.
The newspaper also quoted the document estimating that each asylum-seeker who successfully obtained refugee status could bring on average "four to eight" family members to Germany.
On the basis of the preliminary forecast of 920,000 migrants, some "7.36 million people" could therefore have the right to move to Germany due to family ties.
Interior ministry spokesman Harald Neymanns would not confirm the figures, noting however that the onset of winter could slow the surge in arrivals - as shown in previous years.
Government spokesman Georg Streiter said he was not aware of the document's existence.
Chancellor Angela Merkel has been lauded worldwide for her decision to open Germany's doors to refugees fleeing war and misery.
But within Germany, her popularity is starting to wane as local authorities struggle to cope with the massive task of hosting the record surge in refugees.
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