Toffees manager thinks the defender will be fresh for the summer after missing a chunk of the season injured and hopes his team will be focused on Sunderland rather than the FA Cup
The defender was out injured for two months but has returned to the Toffees team in recent weeks and is looking to get back to his best form before the end of the season.
Moyes told reporters: "In a way, if you are looking at people who could be ready [for Euro 2012], he would be fresh because he missed eight weeks in the middle [of the season].
"There should be no sort of tiredness with Jagielka, that is for sure, and he is a top player. He has played really well.
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"He had one injury which was a medial ligament injury. That was a bad one. It kept him out but since he has come back he has been fine."
The Scot is hopeful that his players will not let thire looming FA Cup semi-final match against Liverpool rule their heads during their Premier League clash with Sunderland on Monday.
"It would be naive if in some way it didn't affect them, but I hope not," he added.
"We are in a pretty good league position [seventh] - better than maybe we thought we were going to be in and we want to try and hang on to that if we can.
"All you can ever do is focus on the next game which is always important.
"We will try and get them focused."