Goldman Sachs Group Inc. 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...