Green delegates meeting in Salzburg were expected to back the coalition already approved by their party leadership and Kurz's Austrian People's Party earlier this week.
If a simple majority of the 276 delegates votes in favor, the Greens will enter the federal government in Austria for the first time.
The party made strong gains in September's national election on the back of growing concern about climate change. It came fourth behind the far-right Freedom Party, the center-left Social Democrats and Kurz's party, which alone received more than 37% of the vote.
The election became necessary after the collapse of Kurz's coalition government with the Freedom Party following the release of a video showing the party's then-leader, Heinz-Christian Strach, offering favors to a purported Russian investor.
Green party leader Werner Kogler has said he wants Austria to be carbon-neutral in 2040, 10 years earlier than the European Union's target.
The Austrian coalition is being closely watched as a possible template for a future government in neighboring Germany, where the Green party has also been riding high in recent polls.