The Gunners have been tracking Monga for some time and negotiations are ongoing, though no deal has been struck yet.
Monga is expected to leave Leicester this summer following the club's relegation to League One, their second successive drop through the divisions.
He is expected to cost around £10m given his unusually advanced experience, having made 30 first-team appearances last season, made his Premier League debut at just 15, and become the Championship's youngest ever goalscorer with a goal against Preston North End in August.
Arsenal are in the middle of an aggressive recruitment drive at academy level this summer, with sporting director Andrea Berta overseeing the operation. The club is also in the process of appointing a new academy manager after Per Mertesacker left earlier in the year, with the successful candidate reporting directly to Berta.
Leicester have suffered two consecutive relegations that have dramatically changed the club's financial position and their ability to retain talent, making young players like Monga particularly vulnerable to departure.
Monga came through the Foxes' academy and attracted widespread attention with his debut season in senior football, his pace and directness catching the eye of several Premier League clubs. Arsenal's decision to move now, ahead of Leicester's first League One campaign, is designed to secure him before a bidding war develops in earnest.
The Gunners are not the only club tracking the forward, though they are understood to be further along in negotiations than their rivals at this stage.