Clarke is desperate to add a creative spark in attack on transfer deadline day after watching his side fail to score in any of their first three Premier League games this season.
The Baggies have been strongly linked with Marseille midfielder Amalfitano in recent weeks and the player will travel to London overnight for further talks tomorrow, according to the Birmingham Mail.
Marseille favour a loan deal for Amalfitano, who has been linked with a whole host of Premier League clubs this summer, including Hull City and Fulham.
Sessegnon is another player who has made West Brom's last-ditch shopping list after being told that he can leave the Stadium of Light.
Sunderland will listen to loan offers for the Benin international, but West Brom are believed to prefer a permanent deal that would cost around £5m.