As the price of the cryptocurrency continues to soar, the Federal Reserve apparently is giving thought to having a product like bitcoin for its own.

William Dudley, president and CEO of the Federal Reserve Bank of New York, said at a conference Wednesday that the Fed is exploring the idea of its own digital currency, according to reports from Dow Jones.

Any product likely would be well off in the future, he said, adding that it would be "very premature" to estimate when the Fed would come up with its own offering, according to Bloomberg.

That sentiment comes even though Dudley said he views bitcoin is "more of a speculative activity" and not a stable store of value.

As the central bank official spoke, bitcoin struck a new high. Just a day after hitting $10,000, it eclipsed the $11,000 mark.

Dudley is not the first Fed official to address the surging popularity of bitcoin.

Philadelphia Fed President Patrick Harker, in remarks made at a conference in September, said he doubted bitcoin would ever undermine the U.S. dollar, primarily because it lacks the backing of a government.

"The paper that's in your pocket, that we call money, only has value because we believe it has value, because we believe the government stands behind it. It's all trust issues," Harker said, according to a Coindesk report.

Earlier in the year, Minneapolis Fed President Neel Kashkari also expressed skepticism about bitcoin ever emerging as a currency, though he said the blockchain technology behind it has "potential" for further development.

Blockchain records digital transactions, key to the trading of bitcoins, which are not actual coins but rather a payment system created online.

The New York Fed did not immediately respond to a CNBC request for additional information on Dudley's remarks.

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