The Japan international is out of contract this summer and St Etienne, who will play in the UEFA Cup next season, are ready to pounce.
ASSE president Bernard Caiazzo told Le Progres: "There is a 90% chance that this boy is going to join us.
"He is a free agent and will bring something special to our team."
St Etienne will look to clinch Matsui's signing this week.