Credit Suisse is quietly pushing to turn one of its trading venues into an exchange, an unusual bid that, if successful, would create the only US stock exchange owned outright by a Wall Street bank.

The plan, which hasn't been made public, is taking shape amid heightened tensions between exchanges and brokers, which compete with each other for trades. Brokers also are big customers of exchanges and are subject to regulation by them through the exchanges' special status as self-regulatory organizations.