Sir John chairs ANZ New Zealand and sits on the board of its parent bank in Australia.
Reserve Bank governor Adrian Orr said the trans-Tasman roles held by Sir John at ANZ and BNZ chairman Doug McKay, who holds similar roles, could raise questions over whose interests are pre-eminent.
Mr Orr said if an Australian parent company got into trouble and a director sat on the Australian and New Zealand boards and the Australian board wanted to bring money back from New Zealand, it would be difficult for a director to act in the best interests of both boards at the same time.
"My biggest concerns with boards is in whose interests are they working? Are they working for the parent shareholder, or the subsidiary shareholder ... that's a real critical challenge," he said.
Mr Orr had already indicated he was planning to rein in the big four Australian-owned banks - ANZ, BNZ, ASB and Westpac - as he believed they were making too much money and posed too much risk to the financial system.
Mr Orr wanted them to hang on to more of their own cash in New Zealand to ensure greater financial resilience. He was proposing doubling the minimum amount of capital held to 16%, though he said he had yet to decide the exact amount or timing.
The big four Australian-owned banks all refused to be interviewed for RNZ's Insight investigation into banking, but their representative organisation, the Bankers' Association, commissioned former Treasury boss Graham Scott to write a submission on the Reserve Bank's capital proposals.
He argued requiring banks to hold twice as much money in reserve would cost the economy about $1.8 billion a year and could lead banks to pull money out of the country.
"Those big banks will have an expected rate of return on their investment in all their activities around the world and if the New Zealand subsidiary is not producing that rate over time, then they'll disinvest in it over time one way or another," Mr Scott said.
While Mr Orr is considering making banking directors choose between New Zealand and Australia, he was not touting the move as a high priority and no decisions had been made.
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The Australian big four banks may have a desired return on investment in their foreign branches, but the reality is all four have spectacularly failed in their overseas businesses. Other than New Zealand.
NAB, National Bank in NZ, lost billions in the UK trying to be as greedy as they get away with in Aus and NZ. ANZ have pulled out of most of their asian business again because they can't compete when faced with reasonably priced competitors.
These four banks perform well when they only compete with each other. They continually offer similar products at similar rates and similar fees and charges. Oh they are always a little bit different, but over all they don't really compete too hard. And shareholder return, PROFIT, is always their number one driver.