The former England goalkeeper only joined the Owls earlier this summer on a free transfer from Wigan Athletic, but is understood to be in talks with Wednesday about terminating his contract due to personal reasons.
Manager Dave Jones already has two experienced goalkeepers on the Hillsborough books, Nicky Weaver and Stephen Bywater playing last night in two pre-season friendlies at Sheffield FC and Stocksbridge Park Steels.
The Owls jet out to Portugal today for a week’s training camp, but it is doubtful Kirkland – who still lives in Lancashire – will travel.
Jones failed in a £250,000 bid for Leeds United Andy Lonergan after the Whites goalkeeper opted for a move to Bolton Wanderers yesterday.
One Owls player definitely on his way is midfielder Liam Palmer who has agreed a six-month loan to League One side Tranmere Rovers.
Scotland Under-21 international Palmer has scored once in 31 appearances for the Owls, but has not featured in the first-team since Jones took over in February.
“I’m really pleased to be able to bring Liam in on loan and thank Dave and Sheffield Wednesday for helping us out,” said Tranmere manager Ronnie Moore.
“He’s a young player who has impressed me.
“They’re keen for him to go out and get games, and we get an energetic, hard-working box-to-box midfielder. It’s a deal that suits both clubs really well.”
French defender Bilel Mohsni, linked with the Owls earlier this month, could be on his way from Southend United after accepting a trial at an unnamed Premier League club next weekend.
The 24-year-old has not returned for pre-season training after being granted an extension of his summer break.
Southend and former Owls manager Paul Sturrock said: “Bilel believes he can play at a higher level and has advised (us) he is very reluctant to return to Southend at all.
“He has ambitions to play at least in the Championship.
“As a consequence, his agent has arranged for him to train with a Premiership club.”
Doncaster Rovers midfielder Paul Keegan, 28, has agreed a new one-year contract to stay at the club.
Burnley have released Zavon Hines after choosing not to take up the option of a second year on the winger’s contract.
The 23-year-old, who is now a free agent, joined the Clarets from West Ham in August 2011 but did not start a Championship game for the club.
Meanwhile, striker Alex MacDonald has agreed a 12-month deal at Turf Moor.
The 22-year-old ended last season on loan at Plymouth, scoring four times in 18 appearances.