LCF collapsed in January 2019, leaving 11,600 bondholders nursing losses of up to 237 million pounds. It was selling "mini-bonds" that raise cash for small firms.
The bonds were not regulated by the FCA, which Bailey heads, but LCF itself and marketing material were.
Elizabeth Gloster, a barrister selected to head the inquiry, said the process of gathering documents for her investigation was nearing completion and the next stage was to interview officials at the FCA.
Gloster told a meeting of over 100 bondholders that Bailey has been chief executive of the watchdog for almost all of the period that LCF was authorised. Bailey is due to take up his new post as governor of the Bank of England in March.
Bailey has already assured her he will be available, Gloster added, declining to say when the interview would take place. Her report is due to be delivered in July.
The FCA will be required to set out key findings, lessons learned and any actions being taken, she added. The FCA declined to comment.
Britain's Serious Fraud Office is also investigating the collapse of LCF.
The Financial Services Compensation Scheme said this month it planned to compensate only 159 bondholders who the body believed 'were given misleading advice by LCF'.
Gloster said her remit does not cover whether bondholders should be compensated but her conclusions will inform the government about whether compensation should be paid.
"I am personally very conscious of the huge personal and financial impact on many of the LCF investors as a result of the collapse," Gloster said.
"We received very sad letters and emails from a very large number of bondholders, some of which make very distressing reading."
By Huw Jones