The Yorkshire Post understands the former Hull City manager is in advanced talks to succeed Jos Luhukay, who was sacked on Friday.
Steve Agnew, Bruce’s assistant, and coach Stephen Clemence were at Hillsborough on Saturday to watch the Owls beat Preston North End 1-0.
If a deal can be finalised Agnew and Clemence could join the club over the Christmas period with Bruce joining them next week after returning from a pre-planned family holiday.
Caretaker manager Lee Bullen – who saw Michael Hector net the winner against Preston – believes Bruce’s record in the Championship would make him an ideal choice for Owls’ chairman Dejphon Chansiri.
Bruce, who also had spells in charge at Sheffield United and Huddersfield Town, has won promotion to the Premier League four times in spells with Hull and Birmingham City.
The 57-year-old was in charge of the Hull side that beat Wednesday in the Championship play-off final in 2016.
“I think if you get the opportunity to speak to someone of the experience of Steve Bruce at this level you don’t knock that opportunity back,” said Bullen.
“At this level I think you can only point to Steve Bruce or our good friend at Cardiff (Neil Warnock) as the ones who just have an unbelievable record of success.
“Steve will be hurting with the way things went at Aston Villa, absolutely, but if you get the opportunity to speak to someone like that – a British coach that knows the Championship inside out – then you don’t knock back the opportunity to speak to him. Whether anything comes of it, I don’t know.
“Let’s see what the next 24 hours hold.
“They are really good football people and I have always had a really good relationship with these guys.”
Hector’s 62nd-minute header gave the Owls only their second victory in 11 games.
Asked how he thought Agnew and Clemence would assess the Owls, Bullen replied: “If they have watched the last five to 10 games, they’d probably think, ‘Geez, we are jumping into the frying pan’.
“But hopefully they will look at that performance against Preston and think, ‘you know what, there is a good team there that has been playing well below par’.
“If they play like that with the discipline they showed against Preston for large spells of the game then it’s not a bad job to potentially be going in for.”
Bullen was due to take training today and tomorrow ahead of the Boxing Day trip to Middlesbrough followed by West Bromwich Albion away on Saturday.
If the deal to bring in Bruce is finalised his first game in charge could be against one of his former clubs Birmingham at Hillsborough on New Year’s Day.
As for Bullen’s own future, the 47-year-old Scot hopes to remain at a club he has served with distinction since arriving in Sheffield in 2004, as both player and coach.
“Everybody knows what this club means to me,” said Bullen. “My dream would be to be part of something for when this club eventually gets back to the Premier League.
“Whether that’s being involved with the Academy, or the first team, or any other role, that would be great.
“If you ask me, ‘do I want to stay?’ Absolutely. But I am not silly – as soon as your ink is wet on the contract you’re a day closer to the sack.
“If he (Bruce) comes in, decides to change, then I will wish the lads all the best, take it on the chin, and I will be sat in the stands at Middlesbrough and West Brom, and bouncing, hopefully.”
Sheffield Wednesday v Preston North End – Big-match verdict: Page 5.