Transfer journalist Ben Jacobs confirmed Arsenal's move, with the club having monitored Monga throughout the season alongside Liverpool, Manchester City and Chelsea.
Monga scored one goal and contributed two assists across 27 Championship appearances, eight from the start, for a Leicester side that will now compete in League One following their second successive relegation.
The teenager is expected to leave the King Power Stadium this summer, with Leicester in no financial position to resist major offers and no prospect of first-team football at Premier League level in the near term. His contract situation and age make him a target under Premier League academy compensation rules, which would ordinarily apply — though the reported £10m-plus valuation suggests Leicester are seeking a negotiated fee above the tribunal baseline.
Arsenal's interest is consistent with their broader strategy of identifying elite youth talent early, a policy that has also brought them into contention for other young players this summer.