The city's public hospital system is jockeying to get one-quarter of the $8 billion in federal funding that the state is slated to get for hospitals.
The cash could help the city's ailing hospitals, such as Brooklyn's Interfaith Medical Center.
The windfall is part of a Medicaid waiver agreement between Washington and Albany.
The head of the city's Health and Hospitals Corporation told the City Council on Thursday that it hoped to receive $2 billion over five years as part of the deal.
"Eighty percent of our revenue comes from Medicaid sources, so it is important that ultimately, the amount of money that is allocated be equitable, and that it reflect in some way the footprint that we represent in the Medicaid program," said Alan Aviles of the New York City Health and Hospitals Corporation.
Both Mayor Bill de Blasio and Governor Andrew Cuomo have said that the money will go to struggling hospitals, perhaps in lower-income areas.
The state Health Department told NY1 that it has not reached an agreement with the federal government on how exactly it would spend the money, so any discussion of a concrete proposal would be premature.