Bolton manager Neil Lennon reportedly wants competition for Ben Amos, who has joined the club on a permanent contract following his release from Manchester United.
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 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.