Bordeaux said in a statement on their website (www.girondins.com) Khazri would travel to England to negotiate personal terms with Sunderland.
The French club said they were actively looking at a number of possible replacements for the French-born 24-year-old who is Bordeaux's top scorer in the league this season with five goals.
Bordeaux are 10th in the 20-team standings.
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Sunderland, second from bottom in the league and four points adrift of safety, signed Ivory Coast central defender Lamine Kone from Bordeaux's rivals FC Lorient this week.
In a busy transfer window for the north-east club, they have also recruited Senegal striker Dame N'Doye on a season-long loan from Turkey's Trabzonspor and defender Jan Kirchhoff from Bayern Munich.
($1 = 0.6980 pounds)
(Reporting by Alan Baldwin, editing by Ed Osmond)
