U.S. District Judge Thomas Griesa, who has ordered Argentina to pay the holdout funds $1.33 billion, is set to preside over the hearing, set for 2 p.m. ET. Griesa has issued an order barring payments to bondholders who participated in the 2005 and 2010 restructurings unless all the holdout investors are paid their award at the same time. The restructured bond holders are due a payment on June 30.
If the payment isn't made, Argentina would enter a technical default on the restructured debt.
Read MoreArgentina on the precipice? Maybe, says S&P
Argentina has been adamant that it will not pay the holdout funds. Kicillof said on Tuesday that they will not negotiate with what he and other officials have called "vulture" funds. The dispute has prevented a resolution to Argentina's sovereign debt crisis since it defaulted on $100 billion in debt in 2001-2002.
Argentina's debt prices fell again on Wednesday after Kicillof said the country wants to swap bonds governed by U.S. law for those governed by Argentine law so they would not be subject to U.S. courts that have made paying existing bondholders more difficult.