The Premier League has been urged to "overhaul" its owners' and directors' test by Amnesty International.
Amnesty described current regulations as "hopelessly unsuited" to proper scrutiny of potential buyers of clubs.
The campaign group said it had sent a new "human rights-compliant" version to league chief executive Richard Masters.
The move comes after the collapse of a proposed £300m Saudi-backed takeover of Newcastle United which had first been agreed in April.
The Premier League declined to comment but is understood to be committed to undertaking regular reviews of its takeover rules.
A consortium, backed by Saudi Arabia's Public Investment Fund (PIF), ended its interest in buying the club last week.
There had been a four-month wait as the bid was scrutinised by the Premier League.
Officials are understood to have wanted more clarity on who would have ultimate responsibility for the club.
The bid was dogged by controversy over Saudi Arabia's human rights record and allegations of TV rights piracy.
It also shone a spotlight on the owners' and directors' test, which measures whether investors in clubs meet certain standards in order to protect football's reputation, and lists disqualifying factors.
Having a criminal conviction prohibits ownership, but there is no morality clause included, and Manchester City's Abu Dhabi-backed takeover in 2008 was approved despite similar concerns over human rights in the United Arab Emirates.
Describing the saga as "a major wake-up call", Kate Allen, Amnesty International UK's director, said the Premier League "urgently needs to get its house in order".
"The current test is hopelessly unsuited to the task of vetting who gets to own and run English football clubs - it needs a serious overhaul," she said.
"At present, anyone wishing to 'sportswash' their reputation by buying into English football can do so knowing that even their involvement in war crimes or torture wouldn't stop them.
"The test simply hasn't kept up with modern trends in international football ownership, not least with foreign powers buying their way into the game.
"Football can be a real force for good… but top-flight football needs to sort out this thorny issue of ownership."
In April, Masters assured Amnesty the league would scrutinise the takeover "with rigour".
In June, Hatice Cengiz, the fiancee of murdered journalist Jamal Khashoggi, wrote to the league to oppose the deal.
Crown Prince Mohammed bin Salman, who is the ruling leader of the country and chairman of the PIF, has taken responsibility for the killing of Khashoggi, calling it a "mistake", but denies he ordered his death.
Masters told Cengiz her objections were being "fully considered".
However, Amnesty says the league's test has "numerous serious shortcomings", with the phrase "human rights" not appearing, despite English football adhering to Fifa statutes that are "committed to respecting all internationally recognised human rights".
Meanwhile, the league is also under pressure from supporters demanding answers about the collapse of the deal.
The Newcastle United Supporters' Trust (NUST) said people in the north-east of England "have been ignored" by the Premier League after the region "missed out on potentially hundreds of millions of pounds of investment".