Goldman Sachs Group Inc. GS 0.02% is weighing a new trading operation dedicated to bitcoin and other digital currencies, the first blue-chip Wall Street firm preparing to deal directly in this burgeoning yet controversial market, according to people familiar with the matter.

Goldman’s effort is in its early stages and may not proceed, the people said. The firm’s interest, though, could boost bitcoin’s standing among investors and fuel the debate around digital currencies, which were initially viewed as havens for illicit activity but are pushing further into the mainstream investment world.

China in recent weeks has banned exchanges that trade bitcoin, fearing the virtual currency could provide an avenue for capital flight. J.P. Morgan Chase & Co. Chief Executive James Dimon, whose bank is the largest dealer in global currencies, last month called bitcoin a “fraud” and said he would fire any employee who traded it.

Yet Japan’s government has embraced bitcoin, creating regulations to legitimize its trading. India and Sweden have mused about creating their own virtual currencies, and the U.S. Federal Reserve has studied bitcoin and the technology underpinning it.

Bitcoin pioneered the cryptocurrency movement, but after eight years, the virtual currency is still struggling to find mainstream acceptance. Author and WSJ Moneybeat reporter Paul Vigna joins Lunch Break's Tanya Rivero to discuss why many people talk about bitcoin, but most don't use it. Photo: Bloomberg

“In response to client interest in digital currencies, we are exploring how best to serve them in this space,” a Goldman spokeswoman said.

Bitcoin is a digital currency that runs on a decentralized network of computers, rather than a centralized ledger under the control of a central bank or government. Users can exchange value directly, without a middleman such as a bank.

Big banks, including J.P. Morgan and Goldman, have dabbled in the technology behind bitcoin, known as blockchain, and opined on its potential to reshape industries. But they have been wary of venturing directly into a market whose early enthusiasts included anarchists and drug dealers.

Bitcoin has been a popular tool of ransomware, like the 2017 WannaCry cyberattack. It was also used extensively on darkweb marketplaces like the Silk Road, which trafficked in illegal drugs. It has also been beset by frauds and Ponzi schemes and its anonymity complicates governments trying to track the people behind transactions.

As digital coins proliferate and draw interest from professional investors, though, they become harder for Wall Street trading desks to ignore.

Bitcoin’s price has soared this year, from $969 to more than $5,000 last month before pulling back. Ethereum, a rival, traded as high as $400 after ending 2016 at $8. In all, nearly $150 billion of digital currencies are in circulation.

Goldman seeks to serve a growing cadre of institutional investors wagering on bitcoin. Its effort could eventually entail a team of traders and salespeople making markets in bitcoins much as they do Japanese yen or Apple Inc. shares.

Keeping abreast of the day-to-day cryptocurrency market could also position Goldman to capitalize on further development of this market. Digital-currency proponents envision a world where coins will be widely accepted by online retailers and companies will use the tokens for cross-border commerce.

Already, cryptocurrencies are infringing on some traditional banking activities. Some startup companies that historically might have hired banks to take them public are bypassing Wall Street by selling digital tokens, rather than shares, to the public. Such “initial coin offerings” raised $1.3 billion over the past three months without paying fees to underwriting banks.

Goldman’s effort involves both its currency-trading division and the bank’s strategic investment group, the people said. That suggests the firm believes bitcoin’s future is more as a payment method rather than a store of value, like gold.

Launched in 2009, bitcoin grew as a communal software project championed by cypherpunks, who embraced its technological promise, and libertarians, who cheered its independence from government influence. In recent years, more sophisticated exchanges have cropped up to host trading, attracting professional investors.

Some 70 hedge funds now invest in cryptocurrencies, according to research firm Autonomous NEXT.

Exchange-traded funds meant to track digital currencies have so far faced pushback from regulators, but they could one day give a wider base of investors a way to indirectly own bitcoin and create new opportunities for savvy traders.

Such interest from institutional investors has propelled the bitcoin market to a size that merits banks’ attention. About $750 million of bitcoin trades on exchanges every day, on par with the daily trading volume of shares of Caterpillar Inc., the equipment maker.

Already, a handful of nonbank finance firms, such as DRW Holdings LLC’s Cumberland Mining and Genesis Global Trading Inc., broker bitcoin trades for institutional investors that want to buy or sell larger amounts than exchanges could handle.

That is a role that banks could easily step into. Wall Street firms also offer leverage to juice trading returns and hold assets on clients’ behalf. So far, though, none of the big banks have dealt directly in bitcoin.

For starters, bitcoin is highly volatile. After doubling in price between July and early September, bitcoin lost 35% of its value in two weeks. That exposes dealers to the risk of big, quick losses.

But it also offers an opportunity for quick-footed traders to profit by anticipating price moves and facilitating panicked trading. Volatility has been sorely missing lately in traditional markets, leading to a slump in banks’ trading revenue.

Goldman, once known as the nimblest trader on Wall Street, has struggled more than peers. Revenue in its fixed-income division fell 21% from last year through June, dragged down by poor performance in commodities and currencies.

Already, some of the infrastructure for trading bitcoin is cropping up. The Commodity Futures Trading Commission this summer approved the first derivatives exchange for cryptocurrencies. LedgerX, founded by two former Goldman traders, will clear options and futures that would allow dealers to protect themselves from drastic price swings and lock in profits.

Many prominent financiers, including Mr. Dimon, believe central banks such as the Federal Reserve will move to shut down digital currencies before they go mainstream enough to rival government-backed notes.

Morgan Stanley Chief Executive James Gorman recently took a nuanced view. He said bitcoin is “obviously highly speculative, but it’s not inherently bad.”

Write to Paul Vigna at paul.vigna@wsj.com, Telis Demos at telis.demos@wsj.com and Liz Hoffman at liz.hoffman@wsj.com