The Blades plan to turnover their playing list and have put Carney along with three others up for transfer as well as releasing four other players.
Sheffield manager Kevin Blackwell is keen to make room for eight players he wants to bring into the squad for next season.
"It's going to be red hot next season, there's no doubt,” said Blackwell.
“The three clubs that have come down are going to be fierce competitors. It's going to be a very tough league, but last year was tough and we finished third.
"It's up to me now to get some new players in. I know there's going to be seven or eight new players coming in, which is more than I would have liked, but that's the way it is."