Fifa sponsor Coca-Cola has told world football's governing body that it wants an independent third-party commission to oversee reform of the crisis-hit organisation, the BBC has learned.
On 9 July the American drinks giant formally requested that Fifa's leadership support the idea.
It wants the commission to be overseen by what it described as "one or more eminent impartial leaders to manage the efforts necessary to help reform Fifa's governance and its human rights requirements".
In correspondence obtained by the BBC, Coca-Cola says: "We believe that establishing this independent commission will be the most credible way for Fifa to approach its reform process and is necessary to build back the trust it has lost.
"We are calling for this approach out of our deep commitment to ethics and human rights and in the interest of seeing Fifa succeed."
The move will put pressure on Fifa's outgoing president Sepp Blatter, who will discuss his preferred reform programme with the body's executive committee on Monday.
Blatter is expected to propose a number of reforms designed to repair Fifa's battered reputation.
These include term limits for members of the executive committee and the president, as well as full salary disclosure for senior officials.
However critics of Fifa have argued that it is so discredited that reform should be taken out of the body's control, and they will be encouraged by Coca-Cola's move.
In May, trade unions and campaign groups wrote to Fifa's eight biggest commercial partners - Adidas, Gazprom, Hyundai, Kia, McDonald's, Budweiser, Coca-Cola and Visa - asking them to speak out about the treatment of workers in Qatar, host of the 2022 World Cup.
The working and housing conditions of migrant construction workers have been heavily criticised.
Soon after, Fifa was plunged into the biggest crisis in its history after twin criminal investigations in the US and Switzerland into allegations of corruption. That led to the arrest of senior football officials, and the resignation of Blatter.
Sharan Burrow of the International Trade Union Confederation said: "Coca-Cola sets the benchmark against corruption by supporting the call for an independent reform commission to rebuild Fifa.
"It's now time for the other sponsors to take a stand against corruption and put the game back on track.
"Football and other sports carry the passions of billions around the world, and can effect real change and solidarity, and corruption has no place in this. The workers enslaved in Qatar need to know a Fifa that will demand fundamental labour rights of this nation.
"We back the leadership of Coca-Cola and call on the Fifa executive to do the right thing on Monday.
"An external reform commission led by a man like [former United Nations secretary-general] Kofi Annan, supported by men and women including sport leaders and players with similar integrity, can make the difference."
Jaimie Fuller of campaign group New Fifa Now said: "Coca-Cola are to be applauded for having the courage to take an ethical stance on something that is so commercially sensitive.
"It's great that Coke understand and respect the power of sport in society and the good that it can do in the right hands.
"This is completely the reverse to the culture within Fifa and Coke's demand for independent reform is a reflection of true leadership.
"This independent reform needs to be led by an eminent person who enjoys the respect and trust of all cultures, whether they be western, Asian, Latin American or African.
"Fifa has shown the inability to reform itself so it must be in independent hands."
Coca-Cola and Fifa's other sponsors contribute around £1bn to the organisation each four-year World Cup cycle.
In the past they have been criticised for not using their influence enough to force Fifa to enact reform. However Coca-Cola's move represents the most serious example of pressure that Fifa has faced from one of its commercial backers, and there are signs other sponsors may follow suit.
On Friday, another sponsor, fast-food giant McDonald's, issued a statement regarding its expectations of Fifa, which it outlined to the governing body last month.
"At McDonald's, we know our customers around the world are passionate about football, and we share their enthusiasm. That's why we've sponsored the World Cup globally for more than 20 years. But recent allegations and indictments have severely tarnished Fifa in a way that strikes at the very heart of our sponsorship.
"As a result, we have expressed our concerns directly to Fifa. We believe Fifa internal controls and compliance culture are inconsistent with expectations McDonald's has for its business partners throughout the world.
"Fifa must now implement meaningful changes to restore trust and credibility with fans and sponsors alike. The world expects concrete actions and so does McDonald's."