The Owls are apparently lining up a move for the 31-year-old centre-back who is expected to leave Blackburn Rovers this summer.
Mulgrew featured 30 times for Rovers last season but could not prevent them from slipping into League One on the final day of the season.
Wednesday have been quiet in the transfer window so far with the arrival of George Boyd adding to the completion of Jordan Rhodes' January loan move from Middlesbrough.
Meanwhile, goalkeeper Jake Kean is nearing the exit door at Hillsborough after Carvalhal confirmed he was in talks with another club about a move.
The battle for young Liverpool winger Ryan Kent is intensifying with Leeds United, Hull City, Sunderland and Aston Villa all among the Championship clubs wanting to secure his services.
Kent was an impressive figure during a season-long loan spell at Barnsley last year where he notched three goals in 44 games.
Leeds are casting their eye over former Celtic youth prospect Aidan McIlduff as they continue to recruit hot talent for their reserve side.
Leeds' Under 23s endured a nightmare campaign at the bottom of the table last year but have made a number of signings in a bid to improve fortunes this year.
McIlduff was released by Celtic earlier this year but the 20-year-old left-back has been given a chance to show off his talents at Elland Road on trial.
Huddersfield Town have been linked with a move for £4million-rated attacker Ante Rebic from Fiorentina – but the move could be hijacked by Brighton and Hove Albion.
Rebic signed for the Italian club in 2013 but has spent most of the last four years plying his trade elsewhere on loan.
Meanwhile, Huddersfield have loaned attacking midfielder Jack Payne out to Oxford United for the season.
The Terriers will have an option to recall the midfielder during the January transfer window.
Paine started ten games in Huddersfield's promotion winning campaign last year, appearing 14 times off the bench.
Bradford City's hunt for a new centre-back will go down to the wire prior to the season start, boss Stuart McCall has admitted.
McCall is hunting a free agent to strengthen the Bantams ranks ahead of their opener against Blackpool with clubs unwilling to do business so close to the season.
“We're always hopeful,” he said. “We would like to think we would have somebody in for next week but I can't positively say we will have.”
Meanwhile, former Bradford City loan star Josh Cullen has been linked with a move to Queens Park Rangers from West Ham.