Edwards and O'Neil each possess previous connections with Wolves
Edwards and Gary O'Neil represent the initial candidates in the frame to replace the former manager as manager of Wolves.
Pereira was sacked on Sunday following the squad's ten-game without a victory beginning to the Premier League campaign.
Furthermore Edwards and O'Neil - both of who have historic associations to the team - are among the options to be evaluated by the club ownership.
Edwards is currently at Middlesbrough, which would pose a possible hurdle to his appointment at Molineux.
However the ex- Luton Town manager - who played over a century of games for the club during his time as a player - is said to be a strong candidate for the position.
The 42-year-old is said to have support from the club directors as they start the process of appointing a new head coach.
Gary O'Neil is also emerging as a surprise contender, although he would be a shock choice given he was released by the club in December last year.
The ex- West Ham United midfielder is currently unemployed which means Wolves would not need to pay any buyout fee.
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