Britain has delayed the appointment of a new BoE governor since last year with the country focused on Brexit – the impact of which remains a big challenge for the central bank – and on an election won by Prime Minister Boris Johnson last week.
Mr Carney, a Canadian, is due to stand down on January 31.
Other names linked with the job have included BoE deputy governor, Minouche Shafik, Shriti Vadera, chair of Santander UK, and former Federal Reserve policymaker Kevin Warsh.
Gerard Lyons, who was economic adviser to Mr Johnson while he was mayor of London, was considered to have fallen short of the requirements of the job but still had an outside chance of getting it, the FT said earlier on Thursday.
Mr Lyons is well known for his pro-Brexit views which are unusual among professional economists.
The British PM rejected Mr Shafik because of her critical views on Brexit, the FT said.
Mr Bailey was deeply involved in shoring up the British banking system during the global financial crisis while at the BoE, and he remains a familiar face to many at the US Federal Reserve and other central banks around the world.
Other roles included helping the BoE to contain the fallout from the collapse of Barings in the late 1980s and participating in the introduction of a new currency in war-torn Iraq in 2003. He has also served as the BoE’s chief cashier.
In his current job at the FCA, he has been criticised for not publishing in full a report into alleged misconduct by bank RBS. Mr Bailey cited privacy restrictions.
His chances of getting the BoE job were seen to have been further dented after the demise of the Woodford equity fund which was popular with retail investors. Mr Bailey has said the FCA was limited in what it could do by European Union rules.
The FT said current BoE deputy governors Ben Broadbent and Jon Cunliffe were still hopeful they might get the top job.