Edwards, a former Wolves defender and one time interim boss, has been linked with the position at Molineux, following the sacking of Vitor Pereira on Sunday, amid Wolves' terrible start to the season.
The 42-year-old emerged as one of the bookmakers favourites for the job earlier this week - and prior to Boro's clash with Leicester on Tuesday night, he distanced himself from the role.
Edwards, who is now the favourite with the bookmakers, was asked about the ongoing speculation again following Boro's 1-1 draw with the Foxes.
And the ex-Luton and Watford boss explained that 'nothing has changed' and his full focus is on the job at Boro.
The Northern Echo has also reported that no formal approach has been made for Edwards, who is under contract on Teesside until 2028.
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They have also said that senior club sources at Boro are confident Edwards will remain at the club, and that his contract does not contact a release clause.
Speaking after the draw with Leicester, he said: "It’s exactly the same, nothing has changed.
“As I keep on saying, it’s my wife and my daughter that are keeping me abreast of it all, I’ve not paid any attention to it at all myself.
“I’m just concentrating on my job here at Middlesbrough. That’s absolutely my only focus, and I’m really pleased with what we’ve delivered over the last couple of days.
“It’s been a difficult turnaround for everyone. I’m really pleased with everyone’s focus. Hopefully, you can clearly see that my mind has only been on this.”