Responding to speculation he could serve beyond June 2019, he told MPs on the Treasury select committee: “Even though I have already agreed to extend my time to support a smooth Brexit, I am willing to do whatever else I can in order to promote both a smooth Brexit and an effective transition at the Bank of England.”
Mr Carney said he expected an announcement shortly.
A spokeswoman for Theresa May responded by saying the prime minister thinks Mark Carney has “done a good job,” adding there would be more to say in due course.
Mr Carney, who was appointed in 2013, originally planned to serve just five years of a maximum eight-year term as governor.
But in October 2016 the Canadian national agreed to stay for an extra year, until mid-2019, to see Britain past its expected departure from the European Union.
He said: “I fully recognise that during this critical period it’s important that everyone does everything they can to help with the transition to exiting the EU.”
His comments follow press speculation that he was in negotiations to stay on until 2020.
Mr Carney also suggested that it might be easier to recruit his replacement once the terms of Brexit were known.
“There are some advantages for that process to be run in the context of full knowledge both of the government of the day and the applicants, those interested parties in the position, of the exact form of Brexit that the country has decided to take,” he said.
Mr Carney also reiterated his belief that Britain’s economy would suffer a shock if the country left the EU without a deal.
Mr Carney previously said that consumer prices would likely rise in the case of a “no-deal” Brexit as companies enacted contingency plans to safeguard their supply chains.
But he added on Tuesday that fewer than 20% of British companies were currently putting in place plans for a no-deal Brexit scenario.
Commenting on Mr Carney’s remarks about his future at the bank, the committee’s chair, Nicky Morgan MP, said: “In his evidence session with the Treasury Committee today, Mark Carney indicated that he is willing to stay as governor of the Bank of England beyond June 2019 if it would assist the Government.
“Stability is vital during this important period. The sooner the Government provides clarity, the better.
“Any extension to Dr Carney’s term should not be used to delay succession planning.”