The 32-year-old goalkeeper has been at Hillsborough since the summer of 2012.
He has been a virtual ever-present throughout his time with the Owls, with the injury problems of his past put to one side.
Kirkland is, however, facing up to an uncertain future as his current contract is due to expire at the end of the season.
No extension talks have been held as yet, but the one-cap England international is prepared to be patient in his pursuit of a new deal.
Kirkland said after Tuesday's 1-0 Championship victory over Brighton & Hove Albion: "I'd love to stay. It's been magnificent since I've been here - the fans have been brilliant, the coaching staff have been superb.
"It's not about individual players, it's about the club, and I'm sure the club will sit down with us - it's not just me, there are a few out of contract.
"When the time is right, I'm sure they'll sit down and decide who they want to keep and we'll move from there. But the most important thing is the team and making sure we are secure. It's about what is best for the club, and that's the way it should be.
"There are five weeks after Saturday left so I'm sure we'll sit down soon.
"It's not just me, there are a lot of players who have been magnificent and we need to keep those players. I'll do whatever the club wants to do - whatever they see fit, I'll go along with that."