The role has been vacant since former chief executive Martin Wheatley’s contract was not renewed in July 2015.
The Treasury said the process is continuing and an announcement will be make in due course.
“We are aiming to make an appointment in due course and will make an announcement accordingly,” a Treasury spokesman said.
Last week the FCA confirmed the Treasury-led recruitment process was ongoing and Ms McDermott will continue as acting chief executive until a permanent replacement has been found, meaning that the contest for the job is no nearer resolution.
Mark Garnier, Conservative MP and member of the Treasury select committee, said: “A conclusion does have to be reached pretty quickly, There is uncertainty for the institution, for people being regulated, and for consumers.”
The Treasury formed a panel to conduct the search and run the recruitment process, which has been advertised externally also.
The panel puts candidates forward to ministers, and the decision rests with those ministers.
Speaking on BBC Radio 4’s Today programme last week, chancellor George Osborne said Ms McDermott had been a very effective interim leader but added the FCA needed “new leadership to take it into its more mature phase”.
He said: “Martin [Wheatley’s] replacement will, like him, need to be passionate about protecting consumers, promoting competition and completing the job of cleaning up the City.”
His comments last week came after back in July, when he failed to renew Mr Wheatley’s contract, Mr Osborne said: “Britain needs a tough, strong financial conduct regulator. Martin Wheatley has done a brilliant job of launching the FCA in tough circumstances.
“Now that phase is complete, the government believes that different leadership is required to build on those foundations and take the organisation to the next stage of its development.
“The government is launching a worldwide search; Martin’s replacement will – like him – need to be passionate about protecting consumers, promoting competition and completing the job of cleaning up the City, so it is the best-regulated market in the world.”
The FCA said Ms McDermott had decided in early December she did not wish to be considered as a permanent successor of Mr Wheatley.
Ms McDermott said: “I have been at the FSA/FCA for 15 years and I remain extremely committed to, and passionate about, the important work we do. It has been, and remains, a privilege to lead this organisation.
“However, going through the recruitment process has made me reflect on what I want to do with the rest of my career.
“As a result I have decided that this is not the right job for me at this stage of my career. This was a decision taken after many months of careful thought and was not one that I took lightly. ”
John Griffith-Jones, FCA chairman, said: “Ms McDermott’s stewardship of the FCA as acting chief executive has served to build on an impressive reputation created during her time leading various divisions across the FCA.
“Over the past few months I have enjoyed working closely with Tracey and have appreciated both her advice and leadership of the organisation. I understand and respect the decision Tracey has made. The board I and will continue to work together with her until the new chief executive is in post.
Ms McDermott has been acting head since Chancellor George Osborne removed Martin Wheatley in July and was widely considered a frontrunner for the permanent role.
She has previously been director of supervision and authorisations and, prior to, was that director of enforcement and financial crime at the regulator.
Meanwhile the Treasury select committee has called for Ms McDermott and Mr Griffith-Jones to appear before the committee to explain why the regulator dropped a review into banking culture last month.
“The FCA’s decision to drop its review of bank culture does seem curious,” Andrew Tyrie MP, the committee’s chairman, said.
