The Daily Mail says Villa are in talks with Lyon over a £19million deal for Traore.
Villa, who have had an offer accepted for Arsenal goalkeeper Emiliano Martinez and remain in discussions with Werder Bremen for attacking midfielder Milot Rashica, had earlier been rebuffed in a £15.7m bid for Traore but have returned with an improved offer.
Traore played 35 matches last season, mainly on the right wing, and scored four goals, adding five assists. He wants to leave though after finding himself frozen out of their Champions League finish last season and spending more time on the bench.
He is keen to join Villa and is excited by the prospect of a return to England.