The Blues have, however, been informed that the Scotland international is not for sale ahead of the close of the transfer window on Thursday.
The 27-year-old joined the Owls from Crystal Palace in 2015 and signed a three-and-a-half year contract extension the following year.
Bannan has impressed during his two seasons at Hillsborough, making 87 appearances and scoring four goals.
The former Aston Villa man has emerged as a fan favourite at the club, and was recently described my teammate Steven Fletcher as "one of the best midfielders" he has played with.
“Baz is right up there in this league and is one of the best midfielders I’ve played with,” Fletcher told the Star.
“I have played with a lot of good players but his vision and passing is great. You can’t get the ball off him; maybe because he’s so small!
“But he has been brilliant since I have been at the club.
“He is in great form and a great player. Whether he has a good or bay day, you know he’s going to give 100 per cent which is the main thing.”
Bannan has so far made seven appearances for Wednesday this season, finding the net in the EFL Cup victory over Chesterfield.