Zaun, 37, has steadily lost playing time to Rod Barajas since Cito Gaston took over as manager last month. He approached general manager J.P. Ricciardi about the possibility of a trade as his starts became less frequent.
"I had a different view of what I hoped would happen this year in Toronto and that was leading the team to a World Series championship," Zaun said after the Blue Jays lost 3-0 to Tampa Bay on Tuesday. "Obviously the situation has changed this year, I'm not the starter anymore."
Ricciardi would happily trade Zaun, but has yet to find a suitor.
"We'll gladly move him if we can find someone who wants him and that's where we're at," Ricciardi said. "Right now there's been no takers for him, there's been no inquiries about him. Maybe he doesn't want to hear that, but that's just the way it is. We know he's unhappy, we're aware of that and if we can move him we will."
Zaun, in the final season of a two-year, $7.25 million contract, is batting .243 with five homers and 21 RBIs in 61 games.
Barajas signed a one-year deal with Toronto this season that includes a $2.5 million option for 2009. He's batting .252 with eight homers and 31 RBIs in 69 games.
Zaun said there'll be no bad feelings if he's still with Toronto once the deadline passes.
"If nobody wants me, than I'll be a Blue Jay until the end of the season and I'll keep doing what I've always done, which is play as hard as I can every single day," he said.