The Australian cardinal, who died on Tuesday aged 81, was one of Pope Francis' top aides until he stepped down to face child sex abuse charges.
The memo was published on a Vatican blog site under a pseudonym last year.
It detailed what the author deemed were failures of the current Pope and a list of priorities for choosing the next.
In the anonymous memo, the author wrote that "Christ is being moved from the centre" of the Church under Pope Francis, and that the Vatican's political prestige had fallen to "a low ebb" under his tenure.
"Commentators of every school, if for different reasons… agree that this pontificate is a disaster in many or most respects; a catastrophe," the memo says.
It says that Pope Francis' decisions and policies were often "politically correct", and accused him of stayed silent on moral issues - like human rights in Hong Kong and mainland China and the Russian invasion of Ukraine.
"The first tasks of the new pope will be to restore normality, restore doctrinal clarity in faith and morals, restore a proper respect for the law and ensure that the first criterion for the nomination of bishops is acceptance of the apostolic tradition," the memo reads.
Italian journalist Sandro Magister, who originally published the memo, on Thursday told Reuters Cardinal Pell had "wanted me to publish it".
Father Joseph Hamilton, Cardinal Pell's personal secretary, declined to comment to several media outlets, saying he was "more preoccupied by [his] grief". A spokesman for the Vatican has also declined to comment.
Pope Francis will deliver a final send-off at a funeral mass for Cardinal Pell on Saturday, as is custom for cardinals.
Earlier this week, The Spectator magazine published what it said was a signed article that Pell wrote shortly before he died. In that piece, Cardinal Pell described the Pope's consultation with the Catholic laity about issues such as church teaching on sexuality and the role of women as a "toxic nightmare".Cardinal Pell was made finance minister under Pope Francis in 2014, and was often described as the Vatican's third-ranked official.
But the cleric left his post in 2017, returning to Australia to face trial on child sex abuse offences, of which he was convicted, then acquitted on appeal. He is the most senior Church official ever to be jailed for such offences.
Cardinal Pell is Australia's highest ranking Catholic, and served as Archbishop of both Melbourne and Sydney before he was summoned to the Vatican.