Barry, 38, won the Premier League with Manchester City and is playing in the Championship for the first time.
The gruelling 46 game fixture list is not easy for a veteran, but Barry believes the schedule has broken right for him this week.
West Brom have had a week's rest since defeat to Sheffield United last weekend, while Leeds played in midweek away to QPR.
Barry told West Brom's official website: "With the full week in between I should be good to go, really fresh, and looking forward to the Leeds game."
He praised the Baggies' medical staff for their flexibility.
He said: "If I don’t feel ready to train or I want to train they allow me to do it, so communication is key.
"I am enjoying it and that has been my approach since the start of the season. I’d never played in the Championship so I just wanted to enjoy it,” he added.
"The lads that have played in the league before said it can be relentless but also fun because you’re playing games."
West Brom's game with Leeds is crucial for the direction of their season.
A win at Elland Road will put them back in the automatic promotion hunt.
Defeat would give them too much ground to make up, and leave them relying on the play-offs.
Have something to tell us about this article?