Der Spiegel quoted an internal document prepared by the German central bank as saying that Europe "will certainly agree a new aid programme for Greece" by early next year at the latest.
The Bundesbank, which declined comment, also described the risks associated with the existing aid package for Greece as "extremely high", according to the report, and said the approval last month of a €5.8 billion aid installment to Athens had been "politically motivated".
The report could not come at a worse time for Merkel, who is favoured to win a third term in the parliamentary election but could fall short of the votes she needs to retain power with her preferred partner, the business-friendly Free Democrats.
Aware that German voters are sceptical about more bailouts, she has repeatedly played down suggestions Greece may require extra aid, or debt relief, despite conflicting views from experts, including at the International Monetary Fund (IMF).
Opposition politicians seized on the report, with Social Democrat budget expert Carsten Schneider accusing Merkel of lying to ordinary Germans due to fears of an election backlash.
"There will be a rude awakening after the election," Schneider said in a statement. "By disputing the need for additional aid for Greece, the Chancellor is lying to people before the election."
The finance ministry declined comment on the report.
As Europe's largest economy, Germany has the largest exposure to Greece, which has received two European Union/IMF bailouts totalling €240 billion.
The loan package is due to expire at the end of 2014, meaning Greece must be able to fund itself on the capital markets by then to avoid the need for additional aid.
"Sand in the eyes"
Bernd Lucke, the head of a new anti-euro party called the "Alternative for Germany", accused Merkel's centre-right government of "throwing sand in the eyes" of voters by refusing to admit the truth about Greece before the 22 September election.
In early June the IMF admitted that mistakes had been made in the first Greek bailout, sealed in May 2010, drawing a rebuke from the European Commission.
In particular, the IMF said international lenders should have considered restructuring Greece's privately-held debt in 2010. Instead, they waited two years to do so, a delay which allowed private investors to sell their Greek bonds and shift the burden to euro zone governments and their taxpayers.
A paper published by the Peterson Institute for International Economics earlier this month is also critical, describing European taxpayers as "the main holder of Greek sovereign risk".
"There is no private 'buffer' left at this point that could protect the European taxpayer from the consequences of a deterioration of the crisis," the paper says.
In recent months European leaders, including Merkel, have praised the work of the Greek government in delivering on the reforms that are a condition of its bailout. But the Bundesbank, according to Der Spiegel, described Athens' performance as "hardly satisfactory".
