The former Wolves player, academy coach and one-time interim boss did not take team training on Friday for Boro's fixture against Birmingham on Saturday and his scheduled press conference was cancelled.
This came after Wolves' had an official approach for Edwards rebuffed by the Championship club on Thursday afternoon, who are still keen to keep their manager.
Talks have taken place between Wolves and Edwards' representatives this week and now, after this latest development, there is an expectation that Edwards will replace Vitor 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.