Edwards has been the subject of an approach from Wolves this week - which was rejected by Boro.
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He will now not take charge of Wolves' clash with Birmingham City on Saturday afternoon.
Boro are third in the table going into this weekend's games.
BBC Sport says Boro management are furious with Wolves' approach and Edwards' apparent eagerness to take up the job.
Boro hired Edwards this summer, handing him a three-year contract after he was axed by Luton Town last season.