The Brazilian international has been at the Turkish side since July 2015 and last season the 28-year-old made 43 appearances in all competitions for his team, scoring six goals.
West Brom's manger Tony Pulis wants to strengthen his midfield, and the Baggies reportedly submitted a £10m bid for the Fenerbache man.
Souza can play in the midfield, as well as right back, and could be on his way to England very soon if the Turkish side accept West Brom's bid.