About a day after the item was first posted on the auction website, the price was at $1,050.
The eBay listing describes the refrigerator as "used" with "signs of cosmetic wear" but "fully operational," the New York Post reported Saturday.
Heather Groll, a spokeswoman for the Office of General Services said she's never seen a government agency sell a morgue cooler.
"Every once in a while, we get an unusual item -- and this would be that," she said. "Whoever buys it would have to come pick it up, so he or she would have to have some familiarity with [refrigerators] like that."
She said the cooler would have to be dismantled to be removed from the room where it is currently housed in the Manhattan Psychiatric Center.
The auction ends in late June, the Post reported.