Asked in a television interview if she thought a deal would come together on Monday and Greece would stay in the euro zone, she said: "At the moment it appears it will go exactly this way."
She added: "I don't think there is a majority to go a different way because a different way is enormously arduous and costs lots and lots of money."
Greece's cabinet on Saturday approved a final set of austerity steps sought by the EU and IMF as a condition for a 130 billion euro ($171 billion) rescue package, raising chances of a deal to avert a chaotic debt default.
"To get this second (rescue) program in place some conditions need to met and this 130 billion has to be financed. This is what is being grappled with now," Fekter said.
The discussions included how much the private sector would contribute, how much will come from the EFSF and ESM safety nets the euro zone has set up, and how much leverage the rescue funds can manage to arrange, she said.
"And above all it is very strictly coupled to conditions that the Greeks must fulfill. For example what is still being discussed now is what in future should supervise (the process) so that the growth path in Greece can be pursued."
At present the "Troika" of the European Commission, European Central Bank and International Monetary Fund oversee how well Greece complies with conditions for bailout money, she said.
"It will be discussed intensely whether these control instruments remain intact or if we create a new control instrument to accompany the Greeks' reform path," she said.
As long as the Greek parliament backs reforms that will eventually put Greece back on its feet after a long, painful reform drive, Europe will stand by Athens, she said.
"The euro finance ministers and, I believe, the heads of government agree that we will not leave Greece in the lurch in the euro zone and also won't throw it out," she said.
Even exiting the euro zone would not solve Greece's problems because Athens would retain a huge debt in euros that would be even harder to repay in devalued drachmas, Fekter said.
And if weaker euro zone countries drop out, then the ones left in a hard core would see exports suffer from a strong currency, just as Switzerland has seen with the strong franc.
"I can understand that this scenario is discussed but it is not the better (way)," Fekter said.
In a separate interview with Austria's Kurier paper at the weekend, EU Justice Minister Viviane Reding also said fellow EU members would rally around Athens in its hour of need.
"Greece cannot go bust, we don't want this," she said, noting the EU treaty has determined the euro is irreversible.
Asked if ministers would sign off on the bailout on Monday, she said: "I am confident they will approve the package, but with conditions. The money cannot flow into a bottomless pit."