Bruce met the Premier League side last week over their vacant managerial position, but the switch has been delayed as the Owls hold out for a compensation package, understood to be in the region of £4m.
The deal would also see assistant manager Steve Agnew and first-team coach Stephen Clemence also depart, less than three weeks before the Owls kick-off their Championship campaign.
Bruce was in the dugout for Wednesday for their pre-season win at Lincoln City on Saturday – the Owls won 3-1 – and hopes the two clubs can thrash out a deal.
“For me, at this particular moment, there is nothing really to talk about until the two clubs reach some sort of compromise,” Bruce said on Saturday. “I’ve had a conversation [with Newcastle].
“It’s happening so quickly that I’ve got to take stock of the whole situation. It’s in the hands of both clubs and we’ll see what develops over the next 24 to 48 hours.
“The clubs have got to agree before any discussions and all the rest of it. Let’s see what happens, I cannot really comment any more than that.
“Out of respect I thought it was only right to go and talk [to Newcastle], it was over with before it started, thankfully the chairman [Dejphon Chansiri] gave me permission to go and have a conversation.
“I don’t really want to talk about dream jobs and all the rest of it, it’s a bit pie in the sky at the moment, I’m the Sheffield Wednesday manager and I have to respect that.
Goals from Jordan Rhodes, Adam Reach and a Neil Eardley own goal gave Wednesday the win at Sincil Bank. A second Owls team won 5-0 at Stocksbridge Park Steels, with goals from Sam Winnall, new signing Kadeem Harris, Atdhe Nuhiu, Fernando Forestieri and Joost van Aken.