The Star understands the Owls lined up Bruce via a third party just over a week ago andÂ are reportedly prepared to offer him a Â£2million-a-year contract to tempt him back into management.
Wednesday are keen to make a quick appointment but sources close to Bruce say he wants to spend Christmas and New Year with his family after a traumatic year in which both of his parents passed away.
Should Bruce accept Wednesday's proposal, it is understood his backroom team of Steve Agnew and Stephen Clemence could precede his arrival.
Bruce, who kicked off his managerial career across the city at Sheffield United and has also taken charge at Huddersfield Town, Wigan Athletic (twice), Crystal Palace, Birmingham City, Sunderland and Hull City during the last two decades, has been out of work since Aston Villa sacked him in October.
The former Manchester United defender has a proven track record of winning promotion from the Championship '“ something he has done four times, with Birmingham Hull twice each. His Tigers team defeated Wednesday in the 2016 Play-Off Final at Wembley after a spectacular second half strike by Mo Diame.
The Owls are looking for a new manager after sacking Luhukay last night. Luhukay, axed after 349 days in charge, struggled in his first job in English football.Â
The Dutchman was shown the door following a run of just one victory in 10 matches. Luhukay leaves Wednesday in 18th position, five points above the relegation zone.
His departure comes just two days after Owls chairman Dejphon Chansiri confirmed he would listen to offers for the club.
In a statement released on the club's website, Chansiri said: 'I would like to place on record my thanks to Jos for the efforts he has given to Sheffield Wednesday.
'But now is the right time for both parties to move on and I wish him all the very best for the future.'
First-team coach Lee Bullen will take caretaker charge of the team, starting with Saturday's home match with Preston North End.