The investor twins have hired engineers from top hedge funds, enlisted a bank and engaged regulators with the aim of opening their exchange - named Gemini - in the coming months, the newspaper reported.
Representatives at Winklevoss Capital could not be reached for comments outside regular business hours.
The Winklevoss twins, who famously accused Facebook Inc founder Mark Zuckerberg of stealing their idea, have been seeking regulatory approval for a Bitcoin exchange-traded fund.
Bitcoin is a digital currency that, unlike conventional money, is bought and sold on a peer-to-peer network independent of central control. Bitcoin is not backed by a government or central bank and its value fluctuates according to demand by users. Users can transfer Bitcoins to each other over the Internet and store the currency in digital "wallets."
Last March, New York's financial services regulator Benjamin Lawsky said he wanted companies that want to operate virtual currency exchanges in the state to submit formal applications, in a step toward eventual state regulation of Bitcoin exchanges.
The New York regulator held two days of hearings with industry participants last January, including the Winklevoss brothers, and said he planned to issue "BitLicenses" to virtual currency firms.
© Thomson Reuters 2015
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