The 32-year-old midfielder signed a season-long loan at Goodison Park from Manchester City on transfer deadline day.
Despite not playing a match during the opening few weeks of the new campaign, Barry insists that he is feeling fit.
"It's a fantastic first game to potentially be involved in but it's the manager's decision because I have not played loads of minutes at the moment," he told the club's official website.
"I feel fit. I haven't missed a day's training and I featured in bits and bobs of the pre-season games."
Everton are currently in 15th place in the Premier League table.