Barry was hot property during his time at Aston Villa, with Liverpool and Manchester City both battling for his signature.
He eventually ended up at the Etihad in 2009, but Wenger says he was keen to bring him south.
Barry faces Arsenal on Monday, when West Brom travel to the Emirates in an 8pm kick-off.
Assuming he starts in the Baggies midfield, he’ll break Ryan Giggs’ Premier League appearance record.
Wenger said: “We were interested in him when he moved from Villa to City but at the time City was the big investor.”