The report said he wants to appear via video link before Argentina take on defending champions France in Doha's Lusail Stadium with an expected global audience of hundreds of millions.
FIFA did not respond to repeated requests for comment, but it is unlikely to give Zelenskiy a platform, given its rules against political messages at the World Cup.
Russia fired more than 70 missiles at Ukraine on Friday in one of its biggest attacks since the start of the war, with Kyiv warning that Moscow planned a new all-out offensive early next year.