While Moyes has no doubts over the 24 year olds ability, he believes the versatile defender must now show he can produce such outstanding performances over a lengthy period of time if he is to really push for an England place.
"He is reliable, consistent and a top drawer defender but probably sometimes hasn't got the recognition or the plaudits that he deserves.
"So it's very good that he has mentioned Joleon's name in terms of playing for England in the future.
"The second season in the Premier League can sometimes be difficult for players who have come up from the Championship but the signs are that Joleon is ready for it.
"He has been showing us in the past week that he has prepared properly and he's looked after himself."
Lescott will become only the third Everton player since the inception of squad numbers in 1993 to wear the number five jersey when the new campaign begins.
"There's no real significance in him being given that shirt," said Moyes. "Dave Watson and Davie Weir were tremendous players for Everton and if Joleon can match their achievements, we will have a tremendous player on our hands."