The potential deal, valued at roughly $33 per NYSE share, is expected to be funded a third by cash, and the remainder by stock.
IntercontinentalExchange had made an unsuccessful joint bid with Nasdaq OMX Group for control of the NYSE last year.
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Shares of NYSE jumped 14 percent in after-hours trading; ICE shares rose 3.1 percent to $132.32.
Spokespeople for NYSE and ICE declined to comment on the report.
NYSE's biggest revenue source is U.S. stock trading, where margins have been under pressure for years. Its plan to combine with Deutsche Boerse, which has a strong derivatives trading business, was blocked by a European regulator due to anti-trust concerns. ICE and Nasdaq withdrew their joint bid in May 2011, citing opposition from U.S. anti-trust regulators.
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ICE's reported plan to buy NYSE on its own may not face the same challenge. NYSE, which operates the New York Stock Exchange, reported $2.8 billion in revenue for the first nine months of 2012, down 19 percent from the same period in 2011, due largely to weaker trading volumes.
Stock trading accounted for half of NYSE's year-to-date revenue, with derivatives contributing 30 percent and technology services contributing the remaining 20 percent.
- Reuters contributed to this report.