West Brom head coach Tony Pulis confirmed last week the club had offered Diaby a chance to stay in the Premier League.
But Diaby, who is currently a free agent after being released by Arsenal earlier this summer, has turned down a move to the Hawthorns.
The 29-year-old spent nine years at Arsenal after joining from French club Auxerre in 2006, but made just two appearances over the past two seasons of an injury-plagued career.
Pulis believed West Brom could be the solution to Diaby’s injury problems, saying: “We’ve had a look and we think there are things he can do to improve his chances of playing 30 Premier League games and we’re confident we can help him do that.”
But Diaby, whose last of 16 international caps for France came in September 2012, wants to return to his home country to rebuild his career.
Arsenal manager Arsene Wenger has described his former player as the “biggest regret of my career”.
“He is a guy who has been severely injured and it is not acceptable, we have paid the price for that but I hope things turn around for him and they go well,” said the Frenchman.