Hungary were ordered by UEFA to play the game in Budapest's 67,000-capacity Puskas Arena without fans as a punishment for the "racist and discriminatory" behaviour of their supporters at Euro 2020, but the governing body allows an unlimited number of school-age children to attend for free.
There have been over 30,000 applications from under-14s across the country, with one adult permitted to attend for every 10 children.
England have also been ordered to play their next home match behind closed doors as a punishment for the chaotic scenes at the final of Euro 2020 and have opened registration to accredited U14 clubs within a 50-mile radius of Wolverhampton for the fixture against Italy at Molineux on June 11. The Football Association (FA) are anticipating a crowd of 2,000-3,000 children.
England travel to Munich to face Germany three days after the game in Budapest, before returning home for two further Nations League ties, against Italy and Hungary, both at Wolves.
UEFA handed Hungary a three-match stadium ban, with the third game suspended, for their fans' behaviour last summer, while they were also hit with a two-match ban by FIFA for the racism which marred England's last visit, a 4-0 win in September.