The 27-year-old forward ended the 2012/13 campaign on loan at Oakwell and helped the Tykes to preserve their second tier status.
Barnsley boss David Flitcroft had been hoping to make the move permanent this summer, but accepts that an agreement with the Owls is now unlikely.
He told The Star: "We put in a bid for Chris with Sheffield Wednesday, but they turned us down.
"I don't think a deal will be done now. We've tried our best to get him, but it doesn't look like it's going to happen.
"They know we want him and we felt we made a good offer, but they told us they don't want to sell him.
"At the end of the day Chris has always been our number one target, but we can't wait around forever. He's a Sheffield Wednesday player, so I've got to be careful about what I say.
"But we've got three or four good options and avenues we're pursuing, so we've got to move on. Otherwise we're going to get left behind."