The blaze happened Eastvale FC’s base in Windygates on Tuesday evening.
Two fire crews were sent to the scene at Greig Park in Milton Road, but the building sustained significant damage.
Police said the boys will be subject to Youth Justice Intervention.
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Sergeant Craig Fyall, of Levenmouth Police Station, said: “This is another reminder of the devastation that can be caused by fire and it is extremely fortunate that no-one was injured on this occasion.
“Eastvale and Greig Park have historically been an important part of the village’s football heritage so it was particularly disappointing to see the facility destroyed by an act of fire raising.
“The response from the community, elected members and businesses following the events on Tuesday to pull together in support of the football club has been quite remarkable and hopefully the facility can be restored as quickly as possible.”