Ms Gray's inquiry into lockdown gatherings in Downing Street contributed to Boris Johnson's downfall last year and prompted numerous Conservative MPs to call on him to resign.
Tory MPs have expressed anger at the job offer, with allies of the former prime minister saying it undermines her report and the impartiality of the civil service.
A Labour spokesman said party leader Sir Keir was "delighted" that "she hopes to accept the role subject to normal procedures".
The government confirmed on Thursday that Ms Gray had left her position as a senior official at the levelling up and housing department.
Under the civil service code, officials of Ms Gray's seniority must wait a minimum of three months before taking up outside employment.
Her report into Partygate, published in May last year, found that staff had partied in Downing Street while the rest of the UK was in lockdown, with the approval of their bosses.
She said many events "should not have been allowed" and the then prime minister, Mr Johnson, "must bear responsibility".
Many people in government praised Ms Gray's professionalism. She also had to investigate her own boss, Simon Case - the head of the civil service - who stepped down from leading the Partygate investigation after reports a party had been held in his own office.
Jacob Rees-Mogg, a cabinet minister under Mr Johnson, has said Ms Gray's Partygate conclusions now looked "like a left-wing stitch up".
However, Labour's shadow culture secretary Lucy Powell told BBC Radio 4's Today Programme it was "ludicrous" to suggest her appointment undermined her Partygate report.
The civil servant does have plenty of experience in government including investigating - and in some cases condemning - powerful ministers.
In his memoir, the former Liberal Democrat minister David Laws recalls being told by fellow minister Oliver Letwin: "It took me precisely two years before I realised who it is that runs Britain.
"Our great United Kingdom is actually entirely run by a lady called Sue Gray, the head of ethics or something in the Cabinet Office - unless she agrees, things just don't happen."
Ms Gray joined the civil service straight from school and worked her way up to the Cabinet Office where, for six years, she led the government's Propriety and Ethics team, which provides advice to government departments on standards issues.
Polly Mackenzie - who worked as a special adviser in the Cabinet Office - told the BBC's Profile programme in 2017: "Sue has been there for so long, she knows everything that anybody has ever done wrong."
Gus O'Donnell, a former head of the civil service, said: "If there is any one person in the civil service who could write their memoirs, hers would be the most valuable, the most priceless and the most sensational.
"I am extremely confident that such a memoir will never be written - her secrets will go to the grave."
In 2017, one of her investigations forced Damian Green - at the time one of Theresa May's most senior ministers - to step down after he was found to have made "inaccurate" statements over what he knew about claims pornography had been found on his office computer in 2008.
She also investigated claims of sexual misconduct by the minister towards journalist Kate Maltby, ruling that her claims had been "plausible".
Speaking to the BBC, Ms Maltby said: "What impressed me most about Sue Gray was how seriously she took her duty of care to complainants... she was determined to listen to junior people, and not let senior staff off the hook.
"I found her profoundly moral in a way that isn't normally seen in Westminster. But she is someone who has spent her life operating in Whitehall, and her report will be limited by the norms of civil service language, the parameters of the task given to her, and by some compromises, especially on transparency, only if minor compromises are required for her to push through her key ethical findings".
Ms Gray's knowledge of ministers' private interests is said to have been useful to prime ministers carrying out rejigs of their ministerial team.
Chris Cook - an ex BBC journalist who now works for news website Tortoise - said one sign of a forthcoming reshuffle would be when Sue Gray's office furniture had been re-arranged.
After 20 years, she left the Cabinet Office on secondment to work at the finance department in Northern Ireland's government.
When a job to lead the Northern Ireland civil service became available she applied, but didn't get it.
Unusually for a normally private individual, she gave an interview to the BBC admitting she was "disappointed" she didn't get the top job and suggested she may have been seen as "too much of a challenger, or a disrupter".
In 2021, she returned to the Cabinet Office leading on matters related to the Union and the Constitution.
She may have spent the bulk of her career in the civil service, but in the late 1980s she did take a career break to run a Northern Ireland pub called the Cove Bar, along with her husband the country and western singer Bill Conlon.
She told the BBC: "I loved it, loved it at the time, I'd never do it again."