The 34-year-old midfielder has made 396 appearances for the Owls since joining in September 2015.
With the club battling relegation back to League One, the Scot says he does not think any of the out-of-contract players have been offered new deals.
“It’s a case of putting the club first,” he told BBC Radio Sheffield.
“I’ve not heard anything, probably all the players out of contract haven’t. It’s a case of knuckling down for these final six games – and what will be will be.
“It’s not a nice situation and I think as a club we need to make sure it doesn’t happen again because it has for the last few seasons now.
“Just having a bit of clarity for players going forward… It’s not a great situation. But you have to put the club first, they are paying your wages and you have to go out and fight for them until your contract is up.”
He added: “It’s at the back of my head at the minute, I’m focusing on winning games.
“If this is the season that my Wednesday career ends, I want to make sure it’s a big season and one to look back on and be proud of.
“I know fighting relegation isn’t something to be proud of but it would be an achievement to stay up after how the season started.”
The Owls are two points adrift of safety and have not left the relegation zone since dropping into the bottom three on 12 August.
A run of four successive wins at the end of February and the start of March boosted their survival hopes but they are now without a win in their past four.
Boss Danny Rohl called Monday’s 2-0 defeat at Middlesbrough a “nothing” performance and questioned his side’s “mentality and attitude”.
They travel to face fellow strugglers QPR, who have won their past two games to move six points clear of danger, on Saturday and Bannan says they have to look forward.
“We’ve had bad performances this season and we’ve bounced back. We need to make sure that doesn’t happen again in the next six games,” he said.
“We’ve watched it back and had hard words with one another. We’ve got to be positive going into the game on Saturday because, as bad as it was, we are one win from getting out of the relegation zone.”
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