Rehn said that football in South America had been especially hard hit, while Africa and Asia were also a concern.
He added: “It is a real danger that the good work that has been done developing football in Asia and Africa could be ruined, so we want to soften the blow and maintain the development that has been done.”
FIFA has allocated $1.5bn to tackle the effects of the pandemic.
Rehn said 150 of the 211 member associations had so far applied for funds but he was concerned that another downturn could not be ruled out.
He said: “The critical thing will be whether a vaccine will be developed and can be used, and that we have medical and other means to fully contain and tame the pandemic, and that is uncertain.
“We cannot rule out worse developments and that would be another ball game if the pandemic were to continue in a severe form next year. Now we are working on the basis of the current scenario.”