Carney, a Canadian who in July 2013 became the first foreigner to head the Bank of England, is stepping down at the end of January 2020.
Carney has already delayed his departure twice to deal with the aftermath of the country's 2016 vote to leave the European Union. The Treasury said his replacement should be announced in the autumn.
Treasury chief Philip Hammond told a committee of lawmakers that his preference is for Carney's replacement to serve the usual eight-year term.
"Stability has a lot of value," he said.
Hammond said he was looking for a candidate who knows his or her way around international organizations, which will be important when Britain leaves the EU.
"It's very important that as well as having someone who can do a first-class job at home we have someone who commands respect in the international arena," he added.
That suggests the search will not just be confined to the U.K.
Among the domestic figures mooted to replace Carney is Andrew Bailey, who heads the U.K.'s Financial Conduct Authority. According to the Ladbrokes betting agency, Bailey is favorite at 2 to 1 to get the job.
No woman has ever been governor of the Bank of England, which was founded in 1694 and which has faced criticism for its lack of gender diversity and the fact that female employees are paid almost 25 percent less than their male counterparts.
There's no shortage of potential female candidates for the top job. Minouche Shafik, a former rate-setter at the bank and currently director at the London School of Economics, is second-favorite at 5 to 1, according to Ladbrokes.
Shriti Vadera, the chair of Santander's U.K. bank arm, is 8 to 1 and Sharon White, the chief executive of the communications regulator, is another strong candidate with odds at 12 to 1.
Looking further afield, the names mooted include Raghuram Rajan, a former Bank of India governor who according to Ladbrokes is third favorite at 5 to 1. Former Fed Chair Janet Yellen has been identified as a potential successor at 20 to 1, while Christine Lagarde, the International Monetary Fund's boss, is an outsider at 50 to 1.
Hammond praised Carney for leading the Bank of England through a volatile period that saw Britain vote in 2016 to leave the EU.
Britain was due to leave the EU in March but the failure of Parliament to agree on a Brexit withdrawal deal means it has been delayed twice. Britain's departure date is now Oct. 31, though Brexit could happen sooner if Prime Minister Theresa May gets her deal approved. The departure date could also be extended again.
Hammond said Carney's "steady hand has helped steer the U.K. economy through a challenging period and we are now seeing stable, low inflation and the fastest wage growth in over a decade."
Though Carney won plaudits for his handling of the economy, he has faced criticism from many Brexit backers for seeming to take sides during the Brexit referendum campaign.
He was accused by some of being overly gloomy when warning of the economic consequences of a vote to leave. The bank recently forecast that the British economy could shrink by 8 percent within months if it crashes out of the EU without a deal.
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