The Algerian defender, valued at a club-record sale by chairman Dave Allen, has already had talks at Athletic but their initial bid did not meet Wednesday's valuation.
According to reports though, Bougherra was in talks with Everton earlier today and the former Crewe man, signed for only £250,000 this summer, could bring in Wednesday's biggest transfer fee in over ten years if a bidding war opens.
In other news, Drew Talbot has completed his move to Luton Town and signed a three-year deal with The Hatters.
Boss Brian Laws says Talbot was down the pecking order at Hillsborough and describes the deal as good business for a player who is not only out of contract in the summer, but also did not play at all last season.