More than 100 applicants are believed to have put their hat in the ring to replace Bruce, who controversially walked out on the Owls earlier this month. Wednesday's hierarchy are in the process of whittling down the lengthy list, with first-team coach Lee Bullen currently standing in during pre-season.
It is understood that Chris Hughton and Tony Pulis have been among names under serious consideration for the role. Both have promotions on their CV's and have worked in the Premier League.
Hughton is thought to have held talks with Owls officials over the possibility of him taking over from Bruce, who quit the Hillsborough club last week to become Newcastle United's new head coach. The 60-year-old has a good track record in the second-tier, having previously won promotion to the top flight with Newcastle and Brighton and Hove Albion.
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But although the former Tottenham Hotspur's full-back is keen to return work, it is understood he wants to manage a Premier League club.
Pulis, meanwhile, left Middlesbrough at the end of last term after 18 months at the Riverside Stadium. His Boro team missed out on a play-off place on the final day of the season after Derby City defeated West Bromwich Albion to seal sixth spot.
Other names who have been heavily linked with the Owls job include Chris Coleman, Nigel Pearson, Gianfranco Zola, Danny Cowley, Gary Rowett and Garry Monk.
It is the third time since December 2017 that Bullen has held the fort on a caretaker basis. However, the popular Scot admits he would be interested in taking the job full-time.
"I think I'd be ready for it," he told BBC Radio Sheffield. "I'm not going to put words into the chairman's mouth and make it more difficult for him.
"I love doing the job, for as long as it lasts. It's a great honour because I see it as my club now, because of the affinity that's been built up.
"I know the infrastructure, the players, and the chairman, but all I'm focusing on is the next two games and we'll see what transpires."
Wednesday round off their pre-season preparations with a friendly against La Liga side Espanyol at Hillsborough on Sunday. Tickets are priced at £15 adults, £10 under 21s and over 65s and £5 under 17s.