Gianni Infantino has indicated a greater amount of money could be distributed to Fifa members from its estimated £4.4bn cash reserves.
In a letter seen by BBC Sport, and sent to the governing body’s six continental confederations on Monday, Fifa president Infantino said he would support “the greatest level of additional funding that can responsibly be delivered”.
Infantino has come under increasing pressure over his aborted Fifa Forward Enterprise (FFE) plan, which proposed selling stakes in the World Cup and other competitions to private investors, sparking a major backlash.
His letter comes after Uefa and Concacaf – the confederations for Europe and North America, Central America and the Caribbean – demanded Fifa pays $10m (£7.5m) to all 211 members from its reserves.
The proposal will be considered by the Fifa Council when they meet on 15 October.
“I will not prejudge the amount,” Infantino said in the letter.
“A single figure can begin the discussion, but it cannot complete a global policy.”
Infantino issued his latest defence of the failed proposal to sell a slice of the World Cup commercial rights that brought calls for his resignation, again claiming it had been intended to generate additional money for the game.
“The recent commercial proposal, now withdrawn, was intended to enable Fifa to invest more in football,” wrote the Swiss-Italian.
Earlier this month, Football Association chair Debbie Hewitt, a Fifa vice-president, told Infantino to release all documents relating to his controversial plan, and called for an independent review of FFE.
Infantino will stand for election for a fourth time in March 2027, with his opponents having until 18 November to find an alternative candidate.