The 21-year old impressed mightily in his loan spell with Ajax last season, helping guide the Amsterdam club to the Europa League final.
His performances have made him a priority for Lyon president Jean Michel Aulas, who proclaimed his objective publicly when unveiling his new signing, Fernando Marcal.
"We want to bring Bertrand Traore to the club," said Aulas.
"There are advanced talks there, but many clubs are interested. We absolutely want to do the deal."
The Daily Mail reports that the clubs have agreed a fee of £16m for the Burkina Faso international.