Dark pools are broker-run electronic trading venues, and several big banks have one. They allow investors to trade anonymously and only make trading data available after a trade, reducing the chance that others in the market will know about the buyer's or seller's intentions and move the price against them.
Dark pool venues have come under scrutiny amid concerns their unlit markets may drive too much volume away from traditional exchanges and make it hard for investors to see demand and potentially distorting prices.
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Last month, Citigroup said it would shut down its alternative stock trading venue LavaFlow, at a time when regulatory scrutiny has increased around broker-run trading platforms, forcing banks to rethink the costs. Wells Fargo shut its dark pool in October, citing a lack of customer demand.
Banks' "costs are skyrocketing and our job is figuring out how we can help them solve that problem," Greifeld told the Journal.
Using its technology, surveillance software and regulatory expertise, Nasdaq can manage dark pools on behalf of banks, still allowing them to trade at lower prices than they do on exchanges and letting bank customers trade anonymously, the newspaper reported.
A final business product hasn't been completed and plans may change, the Journal said.
Read MoreDark pools draw trade away from stock exchanges
Representatives at the Nasdaq were not immediately available for comment outside regular U.S. business hours.
The U.S. Securities and Exchange Commission Chair Mary Jo White announced last year that she planned to propose new rules that would require alternative trading platform operators to disclose more details to the public about the way they operate.