Jagielka was on top form in last weekend's Merseyside derby, keeping Liverpool at bay with a composed display.
Moyes has decided to make Jagielka his captain next season in the wake of Phil Neville's departure and has called on his new skipper to show leadership and become a key figure for club and country.
He told The Mirror: "He sometimes doesn't believe in himself enough or have the confidence he should have when you see how he plays.
"But when you look at the situation with England at the moment, there's maybe an opening in defence for Jags to go and make his own."
The 30-year-old has 16 international caps and has become a regular feature of Roy Hodgson's England squads.