The Scot, outstanding once again in the 2021-22 season, addressed his future in the wake of Monday night's 1-1 second leg draw at Hillsborough in front of just under 33,000 fans - with a heart-breaking goal in the third minute of stoppage-time from Patrick Roberts seeing the Wearsiders progress 2-1 on aggregate to set up a final date with Wycombe Wanderers on May 21.
Bannan, 32, has one year left on his Owls deal and is likely to the club's top earner.
Despite being a player who would walk into a number of higher-division sides - and would be the subject of interest should Wednesday decide that he is available to leave - the midfielder stresses he has unfinished business at the club which is now closest to his heart.
He said: "I’ve got unfinished business, I’ve said that. I wanted to get promoted this season, it hasn’t happened, so I see myself staying here to get promoted next season and giving it another go.
"I wanted to lift a trophy as captain of this club. That’s what I’ll continue to do.
"We’ve come up short, we were a game away from Wembley and that chance to lift that trophy, but it’s unfinished business and hopefully I’m back here to do it again next season.”
"My family are happy and I’m happy,” he said. “I love this club, I’ve touched on it a load of times and that will never change.
"I said at the start of the season that I was going to get this club out of this league and back to where we belong. I need to speak to my family now but I can’t see anything changing. We’re happy, I’m happy and that’s all that matters."