Philip Hammond has spent many idle moments thinking about who should succeed Bank of England governor Mark Carney. How, the chancellor asks himself, can he repeat the stunning, rabbit-out-of-a-hat moment when No 11’s previous incumbent, George Osborne, said in 2013 that the Canadian central banker who was heading the global post-crash clean-up operation was coming to help Britain’s laboured recovery?

Carney is due to step down next June and has said the date is fixed in his diary after already extending his stay by a year to steer the Bank through Brexit and out the other side.

It is a decision that has consolidated his reputation as one of the few senior policymakers taking measured decisions in the national interest rather than the narrow party interest that dominates parliament. So it’s a tall order finding a replacement.

Formally, the process is not supposed to begin for a month. None the less, questions are already being asked about possible candidates.

Before the financial crash, the list of contenders was usually drawn from internal candidates and technical knowledge was the most important item on their CV. In 2019 the appointment will be a politically charged affair that may call into question the independence of the central bank – not least because the winner will be seen by some as a Treasury patsy, willing to implement a policy of cheap money to offset almost perpetual austerity.

Sarah Hewin, chief European economist at Standard Chartered, says the excitement of taking on a multi-layered job that marries monetary policy with a watchdog role over the entire financial services sector will prove attractive to many candidates.

David Blanchflower, a member of the Bank’s rate-setting committee in the years around the financial crash, says Brexit uncertainty and political instability make it a poisoned chalice. It will take a large bag of money to get the best person, he says.

Mark Carney, right, with the man who appointed him, former chancellor George Osborne. Photograph: Suzanne Plunkett/Reuters

“If you want to attract someone with a big reputation, how do you persuade them that they can make a difference when Brexit is still undermining investment and the government is at war with itself? If anything, the job looks like the best way to trash their reputation,” he says. “Still, if you really want an expert with bags of experience of all aspects of financial and monetary policy, Hammond could knock on Ben Bernanke’s door.”

Bernanke is the former head of the US Federal Reserve who is credited with persuading George W Bush and Barack Obama to get the US economy back on its feet with trillions of dollars of government and central bank funds. These days Bernanke is a fellow at the Brookings Institution in Washington and an adviser to fund manager Pimco and the $25bn Citadel hedge fund.

Hewin says: “The environment will be very challenging, but any economist with a policy background would see it as a great time to be involved. So I don’t think it’s a deterrent.”

The urge to find the best in the world will prey on Hammond’s mind, which is why the former head of India’s central bank, Raghuram Rajan, and the ex-boss of Mexico’s central bank, Agustín Carstens, are in the frame. Both have spent time on the committees of international agencies like the International Monetary Fund. Rajan was the IMF’s chief economist between 2003 and 2006. Carstens has just taken a job at the Bank of International Settlements (BIS) in Switzerland that puts him in a role as the central banker’s central banker.

Rajan has ruled himself out several times and Carstens has only just arranged his desk furniture. But Carney refused Osborne’s overtures more than once before being tempted with a big relocation package and the prospect of running a central bank with more powers than any other in the world.

Some have labelled Carney an “unreliable boyfriend” – all promises and no action

Peter Dixon, chief economist at Commerzbank, reckons Hammond need look no further than one of Carney’s former deputies, Andrew Bailey, who now heads City watchdog,the Financial Conduct Authority. Bailey is a calm old-school banker who already knows the ropes inside Threadneedle Street, has emerged from several testing sessions with MPs unscathed and has the respect of market analysts, who believe he understands them.

It makes him the obvious candidate, says Dixon: “Whoever takes over should be judged on the basis of their competence and not their reputation. Bailey has worked in all the main areas and is well respected.”

Dixon warns against a repeat of the Football Association’s mistake when it reached out for the widely admired Fabio Capello to help win the 2010 World Cup. The former Juventus and Real Madrid manager’s reign is now considered one of the worst periods in English football history, though Roy Hodgson’s campaign in 2014 fared little better.

Suren Thiru, head of economics at the British Chambers of Commerce, says Carney has proved to be worse for business that his reputation would suggest. He criticises the inconsistent message from a Bank of England over the last five years that has kept suggesting things will get better, and that on that basis interest rates must rise.

It’s something the next governor must avoid, he says, because it makes business nervous and is a deterrent to investment.

Supporters of Thiru’s view have labelled Carney an “unreliable boyfriend” – all promises and no action. Critics have also cited Carney’s willingness to join highly political projects – like the help to buy scheme, which artificially boosted the housing market – while refraining from open attacks on austerity, when he clearly believes the Treasury should be doing more to support the economy.

Hammond is expected to want the same joined-at-the-hip relationship with his next governor, and for that he will look inside the current set-up. A foreigner with their own agenda might be a risk too far this time.