"I don't think wild horses would keep him from being on that pitch," Kelly told a news conference at the Irish team base in Gdynia, Poland.
Given, who has won 122 caps, was substituted in Monday's friendly against Hungary after missing the May 26 friendly against Bosnia when he travelled to London to have a scan on an injured knee.
After Monday's game, when he was replaced by Kieron Westwood, it was reported by Irish media that Given was also suffering from a calf problem.
"Once you get a little niggle with a knee, you get compensatory issues," Kelly added.
"But anyone who saw the game he played the other night wouldn't question his fitness, form or how sharp he is."
Kelly said that a decision was taken to rest the player after the journey to Gdynia, where the rest of his team mates trained on Tuesday.
He added that there was no risk of a half-fit Given playing against Croatia, only to get injured and miss the rest of the tournament.
"If he's fit to play on Sunday, then he's fit to play," Kelly said. “He wouldn't do that if it meant in any way that it would impair his performance."