The Wall Street Journal says the apartments are owned by private landlords.
The storm displaced tens of thousands of residents from their homes. They've been living in shelters, hotels or with relatives and friends.
Landlords and city, state and federal officials have been negotiating a deal for about a month.
The Journal says some details haven't been finalized. But apartment listings are expected to go live this week on Urban Edge, a no-fee apartment listing website.
They'll be available on a first-come, first-served basis. Storm victims could lease them directly from landlords or have the city place them in housing that meets their needs.
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