Ever since he set his departure date from the Bank of England, there has been speculation about what Mark Carney will do next. There are not that many bigger jobs around than his current one but one of them has become available after the news of Christine Lagarde’s planned departure from the International Monetary Fund for the European Central Bank.

Carney would certainly like a move to Washington, not least because the other job he has had his eye on – prime minister of Canada – is currently occupied by Justin Trudeau. Asked at a Bank press conference whether he is interested, Carney replied he had lots of admiration for Lagarde and that the proper processes should be followed. What he pointedly didn’t say was “no”.

Carney is qualified to run the IMF. He ran Canada’s central bank before his arrival in Threadneedle Street in 2013. He has chaired the Financial Stability Board, the body set up by the G20 to oversee reforms of the global banking system after the near meltdown of 2008. He has been at the forefront of international moves to prepare the financial system for climate-related risks. Philip Hammond says that when Carney speaks at international meetings the other participants put down their smart phones and listen, a courtesy offered to only an elite few.

But none of that might matter, because Carney is Canadian. That’s relevant because under a stitch-up that dates back to the creation of the post-war financial global organisations 75 years ago, a European runs the IMF and an American holds the reins at the World Bank. Carney holds British and Irish passports, and has some influential friends in Europe – Mario Draghi at the ECB for one – but will struggle to make the case that he is European rather than Canadian.

It goes without saying that none of this should have any bearing on who succeeds Lagarde. The right way to appoint a new managing director of the IMF would be to decide what the organisation is actually for and then choose the most suitable person to run it, regardless of their place of birth or their nationality.

For the Fund this means three three things: to return it to its original mission of helping countries out of balance of payments troubles without crippling them with austerity; to help countries meet the 2020 UN sustainable development goals; and to meet the challenge of global heating.

Over the years, and particularly since countries such as China, India and Brazil have become important sources of growth, the US-Europe “gentleman’s agreement” has looked more and more of an anachronism. In 1980, global economic output was split 60-40% in favour of advanced western economies. Today, it is the other way round.

But when the US citizen Jim Yong Kim unexpectedly resigned as president of the World Bank earlier this year, it came as absolutely no surprise that the Europeans left it to the White House to appoint a successor. After rubber-stamping David Malpass for the Bank, the Europeans will expect a quid pro quo from the US when it comes to the IMF.

The process for filling the top jobs at both organisations is supposed to be open, transparent and merit-based, but the advanced nations continue to have a stranglehold on the Bretton Woods organisations. Despite the warm words, everybody knows that Lagarde’s successor will be a European. That’s why Carney wouldn’t have a prayer without a British or Irish passport, and it is why George Osborne, was quick to register an interest.

Osborne would be a terrible choice for the IMF. He showed no interest in the organisation when he was chancellor other than to seek support in Washington for his austerity programme at home. But he knows how the process works. A successful candidate needs to get the backing of their own government and also be well thought of by other countries. The former chancellor will have done his prospects no harm by backing Boris Johnson to be prime minister and has reminded the Europeans that he was quick to back Lagarde when she became IMF’s managing director in 2011. Nor, given the European Commission’s obsession with budgetary orthodoxy, will austerity count necessarily against him.

Even so, the portents for Carney or Osborne getting the IMF gig are not great. Britain has a poor track record when it comes to grabbing the top international jobs; there has never been a Briton heading the Organisation for Economic Cooperation and Development or the World Trade Organisation. As for the IMF, of the 11 managing directors, one has been a Belgian, one a Dutchman, one a German, one a Spaniard, and two have been Swedes. The remaining five have been French, including the last two.

Emmanuel Macron will no doubt be telling fellow EU leaders that Pierre Moscovici, the European commissioner for economic and financial affairs, has what it takes to replace Lagarde but they think it is time for another country to have a turn. In only 12 of the past 56 years has a French man or woman not run the IMF.

The recent horse-trading for the top EU jobs resulted in Germany getting the presidency of the European commission and France getting the plum post at the ECB. Spain and Belgium got the other two jobs up for grabs, which meant there was nothing for eastern Europe.

The signs are good, therefore, for Kristalina Georgieva. She is Bulgarian; she is a former vice president of the European commission; she is number two to Malpass at the World Bank and knows how the Bretton Woods institutions work. And she is good at her job. If it is to be a European, Georgieva ticks a lot of boxes.