Vienna reached "a basic agreement" on a tax deal during talks with its alpine neighbour, Fekter was quoted as saying by the Austria Press Agency on the sidelines of a visit to Portugal.
The minister added that she would travel directly to Bern from Lisbon on Friday to sign the new treaty with Swiss President Eveline Widmer-Schlumpf.
The deal reportedly foresees a flat rate tax of between 15 and 38 percent – depending on the sum involved – on all previously untaxed Austrian capital gains, and in some cases income, in Swiss banks.
Due to take effect on January 1, 2013, the tax deal is crucial to an austerity packaged passed by the Austrian government last month, with a billion euros ($1.31 billion) to be generated through this new agreement alone.
Government estimates put Austrian assets in Swiss banks between €12 and 20 billion.
In late March, parliament approved a €27.9-billion austerity package aimed at balancing the budget by 2016, despite criticism that key measures, such as the tax treaty with Switzerland and a planned financial transactions tax expected to bring in billions of euros had yet to materialise.