The request is the latest development in the dispute surrounding Infantino's abandoned FIFA Forward Enterprise (FFE) proposal. The plan would have created a new company to manage the commercial and ticketing rights for FIFA competitions, including the World Cup, with 21% of the company sold to an investment firm.
The proposal was withdrawn after four days following strong opposition from national football associations.
A letter seen by BBC Sport and signed by UEFA president Aleksander Ceferin and Concacaf president Victor Montagliani said FIFA was expected to end the 2023 to 2026 cycle with reserves of about $6 billion. The two leaders argued that this amount was significantly more than FIFA would need through the 2030 men's World Cup.
They called for at least $10 million to be made available to each member association during the 2027 to 2030 cycle, with the funds directed toward infrastructure and football development.
The proposed one-time distribution would cost FIFA approximately $2.11 billion and would come on top of the organization's regular funding for the cycle.
When the FFE proposal was first presented following the World Cup final, Infantino told member associations they could receive $40 million if they supported the plan. He later set 19 September as the deadline for federations to accept the proposal to qualify for an initial $20 million payment.
Ceferin and Montagliani questioned whether the FFE proposal was necessary to increase funding for football. They said their analysis of FIFA's published financial statements and budgets suggested there was room for a larger distribution from the organization's reserves.
The letter also called for an independent review of FIFA's finances, with access to the underlying financial figures and assumptions.
The UEFA and Concacaf presidents argued that FIFA's accumulated reserves belong to football and should be assessed to determine whether some can responsibly be released for development.
A separate letter was sent to the presidents of the other confederations, including those representing Asia, Africa, South America and Oceania, asking them to support the proposal.
The development follows a letter from Football Association chair Debbie Hewitt to Infantino and FIFA secretary general Mattias Grafstrom, requesting the release of documents relating to the FFE plan.
Infantino is seeking a fourth term as FIFA president in March, while potential opponents have until 18 November to nominate an alternative candidate.
