As chief operating officer, Lamour is two layers of management below Infantino.
In his – which has been seen by BBC Sport – Lamour said “what has been announced in recent days and what has been happening behind the scenes in recent months defies belief and imagination”.
“It is becoming increasingly difficult for Fifa’s administration to work under these conditions and fulfil its mission,” he wrote.
“I have no authority to speak on behalf of my colleagues, and perhaps I am mistaken. But my feeling is that we all want to be proud to work for Fifa, and today, unfortunately, it seems that is no longer the case for many of us.
“I know I have a duty of loyalty to my employer. But I also, and above all, have a duty of loyalty to certain values and to support my colleagues.”
Lamour joined Fifa in November 2024, having previously served as deputy general secretary at Uefa.
Cordeiro, meanwhile, had been a Fifa senior adviser for four years and 11 months.
He represented the world governing body on the White House taskforce for the 2026 World Cup and was a former investment banker with Goldman Sachs.
Appointed in September 2021, he 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”.
“The proposal has become a defining question for Fifa’s future,” he wrote.
“Fifa’s responsibility is not to maximise commercial returns at any cost. It is to protect and strengthen football for future generations.
“When those principles come into conflict, football must come first.”
Cordeiro said he had no involvement in this proposal.
“Most troubling of all is the absence of answers to fundamental questions,” he added. “Why this deal? Why now? What oversight exists? Who benefits?” he wrote.
“These questions remain largely unanswered, and yet member associations are being asked to make a decision of enormous consequence in barely 50 days or risk being left behind.
“That is not a responsible way to determine the future of the world’s game.”