Full-back Leigh and winger Drury are highly rated within the corridors of power at the Etihad Stadium.
Both players are yet to make a first-team appearance for City, but are tipped for big futures in Roberto Mancini's squad.
Drury is currently on loan at Burton Albion with City's coaching staff keen for him to gain some first-team experience.
18-year-old Leigh has been a regular in the Academy and elite development side and he has impressed in their FA Youth Cup campaign this season.
City are now set to reward the young pair with new two-year deals to keep them at the club.