According to the Sonntagszeitung newspaper, the two sides will ink an agreement on August 10 which will allow for income from dividends and interest on funds deposited in Swiss accounts to be taxed, the newspaper said.
Although the exact tax rate has still to be finalised it is likely to amount to around 25-26 percent, the report added.
While the German press reported recently that the Swiss banks could have to pay 10 billion euros to the German tax authorities in compensation for tax evasion over the last decade, the actual sum would be around two billion Swiss francs (€1.8 billion/$2.5 billion) under the accord, Sonntagszeitung said.
Such an agreement would not only allow for the resolution of the tax dispute between the two countries, but also legalise the assets deposited in Swiss banks by German nationals and allow them to remain anonymous.
A similar agreement could also be soon signed with the government in London which would see the British tax authorities paid around 500 million francs, said the newspaper.
The Swiss and German governments, whose ties have been soured for some time by the dispute, have been negotiating a dual taxation agreement for several years, which should in future help identify tax evaders.
The German authorities have made tackling tax evasion in both Switzerland and Liechenstein a major priority in recent years, controversially paying for secret banking data stored on stolen computer discs.
Tax officials say they recovered €1.6 billion last year from taxpayers who had been identified through the data.
Some Swiss banks have struck their own agreement with the German authorities such as the private Julius Bär bank which agreed in April to pay €50 million to end tax evasion probes against it and its employees.