London, 24 August — The 41-year-old has asked for time to consider their offer and has said he will make a decision over the weekend.
Henry, who left his role as a Sky Sports pundit in the summer to concentrate on his coaching career, was linked with the Aston Villa job earlier this summer.
The Frenchman has been working as an assistant to Belgium boss Roberto Martinez since 2016 and was part of the backroom staff that led the team to third place at the World Cup in Russia.
The Ligue 1 side recently suspended manager Gus Poyet after he was critical of a transfer that had been made without his knowledge.
Bordeaux sold striker Gaetan Laborde to rivals Montpellier and Poyet reacted furiously after their Europa League win over FC Mariupol, labelling the transfer "a disgrace".
Poyet was suspended for a week with Eric Bedouet taking over for Sunday's league clash with Toulouse, which saw Bordeaux fall to a 2-1 defeat.
Henry played in Ligue 1 between 1994-1999 with Monaco before moving to Juventus.
The former France forward made 254 appearances for Arsenal between 1999 and 2007 and won 123 caps for his country.
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