The 28-year-old has only won six caps for England, but impressed in the 4-0 win over Bulgaria last month.
“I think Jagielka has given a fresh impetus to England,” said Moyes.
“I think Rio Ferdinand is a top player, as is John Terry, and England have a strong base at centre-half. But I do think Jags has come in and done well.
“It’s like a team manager when he leaves out one of his better players and puts in someone who does well.
“That leaves you with the dilemma of whether to give the boy a chance or go back to the player who was left out.
“From my point of view, Jags got better in the England games. His confidence grew and he gives England something different at the back.
“He is quick around the ball and would play well with John Terry or whoever he is paired alongside.”
