The 34-year-old goalkeeper is on the lookout for a new club after turning down a one-year contract extension at the Championship outfit.
“This has been a really tough decision and one that I have mulled over through the summer but I have decided to move on,” the former Liverpool goalkeeper told The Sheffield Telegraph.
“I want a new challenge at this stage of my career. Everyone loves to play first team football and I am no different.”
Chris Kirkland stats
Kirkland joined Wednesday on a free transfer in the summer of 2012 after leaving Wigan Athletic.
The Englishman made 35 appearances in the Championship during the 2013-14 season, keeping eight clean sheets in the process.
The former Liverpool custodian made 2.40 saves per game and 1.68 saves per goal on average.
During the 2014-15 campaign, Kirkland could make feature in just four Championship games for Wednesday.
The 34-year-old made 2.25 saves per game and 1.80 saves per goal for the Owls last season.
Wednesday finished 13th in the Championship last season with 60 points from 46 matches.
Carlos Carvalhal was named the Owls head coach earlier this summer following the departure of Stuart Gray.