According to the Financial Times, May gave her approval to the idea which would likely see Carney remain in the role until the second half of 2020.
Chancellor Philip Hammond confirmed that Carney's term has been extended until 31 January 2020, a further seven months on his original deal.
He had originally only meant to remain for five years after joining in 2013, but announced plans to stay an extra year four months after the Brexit Referendum in June 2016. He has been accused for much of his time at the bank of botching messages on policy. With the March Brexit deadline looming, the UK's future relationship with the European Union remains unclear, while Prime Minister Theresa May's current plan is proving unpopular with lawmakers both at home and overseas. Some economists have raised doubts about the case for rate hikes amid mixed economic data.
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In remarks that will remind Brexiteers why they find him so frustrating, Mr Carney warned that a no deal Brexit would send prices rising and hit real incomes.
'Accordingly, I am willing to do whatever I can in order to promote both a successful Brexit and an effective transition at the Bank of England and I can confirm that I would be honoured to extend my term to January 2020. Female candidates mentioned include Sharon White, head of the communications regulator, and Santander U.K. Plc Chair Shriti Vadera. However, it is understood they now have a good relationship.
Should Brexit go smoothly and United Kingdom economic activity pick up steam in 2019 a Carney-led Bank of England would nearly certainly accelerate the pace of interest rate rises as per recent guidance. The former Bank of Canada chief was appointed to the role in late 2012 after previously saying he wasn't interested in the job, and initially agreed to serve just five years of what is usually an eight-year term.