The veteran is set to break the Ryan Giggs' Premier League appearance record against the 'Gunners' on Monday night but things could have been very different for the 36-year-old.
The former England international claims that he almost joined Arsene Wenger's side when he left Aston Villa for Manchester City back in 2009 and then again when he moved to Everton in 2014.
"There were a couple of conversations with representatives and Arsene that he was interested," Barry said.
"Before I was leaving Villa and when I was leaving Man City to go to Everton there was a bit of interest too.
"But it didn't materialise. I've got massive respect for Arsene Wenger for what he's done for the English game and it would have been good to work under him, but that didn't happen.
"He deserves credit because he was ahead of the game back then. If you speak to people who worked with him in the late 1990s, he was seeing things and doing things that other managers in England weren't.
The exprienced midfielder says that he could have stayed with Everton this summer but says that he is still as keen as ever to play first-team football, hence his switch to the Hawthorns.
"Part of me thought, 'This was going to be the easier way to end your career'," he added.
"There's less pressure on you, you're not going to be starting games and less expected of you.
"But the other part of me thought, 'It's going to be too easy going down that road - come to West Brom for another challenge'.
"It might be harder, a tougher challenge, but I didn't want to slowly go down that road of fizzling out."