But probably not Stanley Fischer.
While he was born in what is now Zambia, he holds dual citizenship with the US and Israel and was a former governor of the Bank of Israel as well as having served as chief economist at the World Bank, so while he may not be a Gentile, he does appear to be more than qualified to serve on the Fed Board of Governors. He also has degrees from the London School of Economics (but then so does Mick Jagger) and MIT.