The Owls had previously rejected a £1.3m offer for the 24-year-old, who had a spell on loan with Crewe last season, making 12 appearances.
The Algerian international has been in fine form for the Owls since joining from French side Gueugnon in the summer and has been an ever-present.
Birmingham and Everton have also expressed an interest in signing Bougherra.
However, only Charlton made a firm offer and the player is now expected to travel to London for talks and a medical.
Owls chairman Dave Allen declared earlier in the week that he would only listen to offers of around £3m for Bougherra.
It is rumoured that the deal could be £2 million with another £500,000 should the club retain its Premiership status.
Have The Addicks finally got their man? Have your say now.
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