Bruce only joined Wednesday in January, guiding them to a 12th place finish in the Skybet Championship.
Newcastle United are without a manager after Rafael Benitez opted not to sign fresh terms at St. James’ Park following the expiration of his contract at the end of June, instead opting for a move to the Chinese Super League with Dalian Yifang.
Bruce has a wealth of experience managing in the Premier League after spells at Wigan Athletic, Birmingham City, Hull City and Sunderland.
Bruce held talks with Newcastle United officials over the weekend but was in charge of Wednesday’s 3-1 over Lincoln City on Sunday.
"It’s in the hands of both clubs,” the 58-year-old former Manchester United defender said of his future.
“We will see what develops over the next 24 to 48 hours.
“At this particular moment, there is nothing really to talk about until the two clubs reach some sort of compromise.”
If the deal goes ahead as expected, Newcastle United will be the 11th club Steve Bruce has taken charge of in his managerial career.
Bruce will bring on board two of his assistants at Sheffield Wednesday, Steve Agnew and Stephen Clemence, who have also left their posts at the Championship club.
Newcastle United are already in China preparing for the Premier League Asia Trophy game against Wolverhampton Wanderers on Wednesday.
