The 39-year-old is understood to have been back into Rockcliffe for talks on Tuesday following an initial interview three weeks ago, and is close to being appointed.
He is set to be joined by Steve Round, who will return for a second spell as assistant manager, while Leo Percovich is also close to arriving for another stint as goalkeeping coach.
A Boro legend as a player, Woodgate had been one of Tony Pulis’s assistants until the Welshman left the job at the end of the season after they missed out on the Sky Bet Championship play-offs.
Woodgate had retired from his playing days at Boro – his boyhood club – in 2016 and was immediately given a job among the academy coaching staff.
Boro owner and chairman Steve Gibson has a track record of giving the club’s top former players a chance as at management, having introduced both Bryan Robson and Gareth Southgate to the role.
Ex-England centre-back Woodgate, who went on to play for Real Madrid and Tottenham in a successful but injury-plagued career, looks to be the next man given his first foray into management.
Woodgate came through the ranks on Teesside before switching to Leeds in 1996 and breaking into senior football at Elland Road, and he also had spells at Newcastle and Stoke before retiring at 36 at the end of the 2015/16 season.
Meanwhile, Round was previously assistant to Steve McClaren at Boro from 2001 to 2006 and followed him to England before working with David Moyes at Manchester United and then a spell as director of football at Aston Villa.
Percovich was goalkeeping coach under Aitor Karanka, who has also been linked with a return to the club but is understood not to have held talks with Gibson about doing so.