Reports emerged on Thursday that Sam Allardyce had turned his attentions towards the Tunisia international after failing to strike a deal with Swansea City over Andre Ayew.
Everton and Aston Villa had also been linked with Khazri but Sunderland are in pole position to complete his signing after Bordeaux confirmed the clubs had struck a deal.
"The club has reached an agreement with Sunderland for the transfer of Wahbi Khazri," a statement released by the Ligue 1 club on Friday read.
"The playmaker has a great opportunity with the English club. We have therefore allowed him to negotiate.
"At the same time, Bordeaux are actively working along several tracks to find an attacking replacement for the Tunisia international."
Sunderland are reportedly to pay between £8million and £9m for the 24-year-old.