Infantino became Fifa president in 2016 when he beat AFC president Sheikh Salman al-Khalifa by 115 votes to 88.
Fifa’s next president will be confirmed at the organisation’s 77th Congress in Morocco next March. Candidates have until 18 November to put their names forward.
Prior to this week, it had been anticipated Infantino would be re-elected unopposed. Associations around the world, including some in Europe, had already confirmed their intention to vote for him.
It remains to be seen if the events of this week will result in a mass withdrawal of their support.
In his statement, Infantino reiterated his plan was designed to strengthen members associations, “especially in countries where support is most needed”.
He added: “Our purpose has always been – and always will be – to unite and improve.”
However, the proposal clearly created division within Fifa itself.
Cordeiro, who represented the world governing body on the White House taskforce for the 2026 World Cup, is the first senior figure at Fifa to resign over the plans.
In a lengthy statement, Cordeiro said he “unequivocally” opposed the plans and said he “did not accept the proposition” Fifa needed outside investors to “unlock greater value”. He added he had no involvement in the proposal.
It is understood Infantino even left some of Fifa’s eight vice-presidents in the dark about his plan, which it is claimed could have raised $10bn (£7.5bn).
Lamour called it “the project of one person” and said “a president must bring people together, unite them, and inspire them” but this was “the opposite”.
“If that means I lose my job, then so be it,” he added. “I will understand and respect that decision. At least I’ll sleep well tonight.”