Mark Carney is 'right man for the job', PM believes
Prime Minister Theresa May believes Mark Carney is the right person to be Bank of England governor, her official spokeswoman has said.
Mrs May is "supportive" of him continuing in his role until 2021.
Pressure has been building on Mr Carney to clarify how long he intends to stay in the job.
Newspaper reports over the weekend suggested he was planning to leave in 2018. However, he is now thought to be leaning towards extending his tenure.
BBC economics editor Kamal Ahmed said: "All the people I've spoken to, close to Mark Carney, suggest he is more towards staying than leaving."
When Mr Carney became governor in June 2013 he committed to serving for five years. Since then he has made clear he is considering extending his stay, saying he would clarify at the end of this year whether he would stay for the full eight-year term that governors usually serve.
Some reports suggest he would like to stay to steer the UK through the challenges of Brexit. But he told a House of Lords committee last week that should he decide to go it would be an "entirely personal decision". Mr Carney has a wife and four daughters, who moved to London with him in 2013.
Speaking to reporters, Mrs May's spokeswoman said: "The PM has been clear in her support for the governor, the work he is doing for the country.
"It is clearly a decision for him, but the PM would certainly be supportive of him going on beyond his five years.
"The PM has always had a good working relationship with the governor of the Bank of England and intends to continue that."
Asked if Mrs May thought Mr Carney was "the right man for the job", the spokeswoman replied: "Absolutely."
It is thought Mr Carney might make an announcement on Thursday, when he holds a news conference following the publication of the Bank's Quarterly Inflation Report and the announcement of the result of its latest interest rate meeting.
Analysis: Kamal Ahmed, BBC economics editor
Nothing I have heard over the last few weeks - and I have spoken to many people in Mr Carney's inner circle - suggests to me that the governor wants to leave in 2018.
To announce now that he will go in two years would see power immediately begin draining away.
The markets would also be left with a further layer of uncertainty to contend with.
And the voices of those politicians such as Jacob Rees-Mogg, a member of the Treasury Select Committee, and Lord Lawson, the former chancellor, who think the governor should resign immediately given his economic warnings before the referendum, would only become louder.
I think Mr Carney would also see it as a personal defeat.
The governor of the Bank of England, not staying to make Brexit a success, which he says it can be, but walking off the pitch at just the time the markets are calling for economic stability and certainty.
Over the weekend, the Bank of England reiterated that Mr Carney would make his decision public by the end of the year.
According to the Financial Times, one of the reasons Mr Carney wants to stay on is to defend the Bank of England's independence against attacks from pro-Brexit campaigners who have argued that the Bank produced deliberately gloomy economic forecasts to support the Remain campaign.
Conservative MEP, and prominent pro-Brexit campaigner, Daniel Hannan, has suggested he should leave his post.
"If he does stay, it's got to be on basis that he's not the rock star banker who presumes to tell Scotland whether to stay and Britain which way to vote, but rather sticks narrowly to his brief," Mr Hannan told BBC Radio 4's Today programme.
Many politicians have made it clear they would like Mr Carney to stay on, arguing that it would provide welcome continuity for business and the economy and may help counter any uncertainty caused by the Brexit negotiations.
Speaking to the BBC on Sunday, Business Secretary Greg Clark said: "I think Mark Carney has done a tremendous job, a fantastic job, during his tenure there. It is clearly a decision for him."
Mr Clark was financial secretary to the Treasury when Mr Carney was appointed by the then Chancellor, George Osborne, in November 2012.
"I think it was a brilliant appointment," Mr Clark said.