Analysts expect that Britain voting to leave the EU is likely to result in sterling losing up to a fifth of its value.
"All the banks are looking at this very actively," he told the Reuters Regulation Summit Bailey today.
Bailey, who is set to start his new job as chief executive of the Financial Conduct Authority in July, went on to say that London has no "God given" right to remain a global banking centre if Britain were to leave the European Union.
"We need a banking system to support the domestic economy but I am afraid we don't have a God-given right to have anything in terms of international. That decision will be taken by many actors over time," he said.
London is home to over 250 foreign banks making it one of the world’s biggest financial sectors employing thousands of people.
Last week Bank of England governor Mark Carney sparked controversy by saying that Brexit could lead to a recession. He said that it was the Bank of England's "responsibility" to talk about the impact of Brexit as it is probably the "biggest risk" to the UK economy.