"By the time the offer expires on Friday, the number of approvals will be significantly over the minimum required," Finance Minister Hans Jörg Schelling said.
"The risk of bankruptcy for the southernmost province should thereby be averted," his office said in a statement.
The Austria Press Agency quoted Schelling as saying that more than 75 percent of so-called senior bondholders -- above the two-thirds minimum --have already given their assent.
Carinthia's state bank Hypo Group Alpe Adria (HGAA), having embarked on a high-risk expansion under far-right former governor Jörg Haider, had to be nationalised in 2009 after the global financial crisis.
Its €11 billion ($12.3 billion) of debts were transferred into a special "bad bank" vehicle called Heta, but Carinthia was the final guarantor and payments were threatening to drag the state of 500,000 inhabitants into bankruptcy.
An offer to senior bondholders to swap their debts was rejected by creditors earlier this year, but central government sweetened to the deal to 75 percent of the value of the bonds in cash or 90 percent in Austrian government bonds.