The midfielder made a deadline day loan switch from City to Everton FC
The Goodison outfit resume Premier League hostilities after the international break when they host Europa League winners Chelsea on Saturday evening.
Barry has not played a competitive match since May 14 having been told he was no longer part of new Manchester City manager Manuel Pellegrini’s long-term plans.
But the 32-year-old, who signed on a season-long loan from the Etihad on last week’s transfer deadline day, believes he is fit enough to be thrown straight into the fray.
“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,” said Barry.
“I feel fit. I haven’t missed a day’s training and I featured in bits and bobs of the pre-season games.
“The season’s a well underway now and I’ve not played but I am confident If asked to play I can do a good job.”
Meanwhile, returning Everton favourite David Unsworth believes the old Bellefield spirit is alive and kicking at Finch Farm.
Unsworth, who made more than 300 appearances in two spells at the club as a player, was named assistant to under-21 manager Alan Stubbs on Monday.
The former defender had departed three years before Everton moved from their Bellefield training ground to the new facility in Halewood.
But after only a day at his new home, Unsworth has already recognised the famed spirit that has become synonymous with the Goodison outfit.
“It’s great to see so many familiar faces and I was made to feel very welcome on my first day, I can assure you,” he said.
“The facilities are brilliant, I have to say. Bellefield did have its place and at the time that was a great place to be and work, and there was a great feeling there.
“But this place has got that feeling as well because you take those characters with you – the kitmen, the ground staff and so on – and you put them in a new building and they recreate it and make new memories.
“Time has moved on and Finch Farm is phenomenal.”