Edwards together with O'Neil each possess past links with the club
Edwards along with O'Neil represent the initial names in the frame to succeed Vitor Pereira as manager of Wolves.
Pereira was sacked on the weekend after the team's ten-game winless start to the top-flight campaign.
And both candidates - both of who have historic links to the club - are part of the options to be evaluated by the club leadership.
Edwards is presently at Middlesbrough, which would pose a possible obstacle to his appointment at Molineux.
However the former Luton Town manager - who played more than 100 of appearances for Wolves during his playing career - is said to be a strong contender for the vacancy.
The 42-year-old is reportedly enjoys backing from the Wolves directors as they start the process of appointing a fresh head coach.
Gary O'Neil is also appearing as a unexpected contender, even though he would be a shock appointment considering he was sacked by the club in the previous winter.
The ex- West Ham United player is out of work which means Wolves would not need to pay any buyout fee.
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