The former Wolves defender and interim boss has emerged as the front runner to replace Vitor Pereira - who was axed on Sunday.
On Friday, it was confirmed that Edwards, who has previously won promotion to the Premier League with Luton Town, had not taken Boro training as negotiations continued over a move to become Wolves head coach.
The one time Wolves interim boss also saw his scheduled press conference on Friday cancelled.
This came after Wolves' had an official approach for Edwards rebuffed by the Championship club on Thursday afternoon, who are keen to keep their manager.
Talks have taken place between Wolves and Edwards' representatives this week and after Friday's development, there is an expectation that Edwards will replace Pereira as Wolves' new head coach.
However, Wolves still have to overcome the hurdle of paying compensation to Middlesbrough if Edwards is to be released from his contract.
And on Saturday morning it was stated that Edwards had been 'stood down' from taking charge of Boro's clash with Birmingham amid the Wolves interest.
According to reports, Edwards was planning to take the game but the club have decided against it.