Details of the platform that Intercontinental Exchange is working on have not been finalized and the project could still fall apart, given the hesitancy among big Wall Street institutions to be closely associated with the Wild West of virtual currencies. A spokesman said that the company had no comment.

Many corporations and governments have expressed interest in the technology that Bitcoin introduced, particularly a form of database known as the blockchain.

Some large financial exchanges, including the Chicago Mercantile Exchange, have already created financial products linked to the price of Bitcoin, known as futures. But the new operation at ICE would provide more direct access to Bitcoin by putting the actual tokens in the customer’s account at the end of the trade.

ICE has had conversations with other financial institutions about setting up a new operation through which banks can buy a contract, known as a swap, that will end with the customer owning Bitcoin the next day — with the backing and security of the exchange, according to the people familiar with the project.

The swap contract is more complicated than an immediate trade of dollars for Bitcoin, even if the end result is still ownership of a certain amount of Bitcoin. But a swap contract allows the trading to come under the regulation of the Commodity Futures Trading Commission and to operate clearly under existing laws — something today’s Bitcoin exchanges have struggled to do.

The chief executive of Nasdaq, Adena Friedman, recently said her company could also create a virtual-currency exchange if regulatory issues are ironed out. While several hedge funds have been buying and selling Bitcoin, most large institutional investors, such as mutual funds and pensions, have avoided it largely as a result of similar regulatory concerns.