The Argentine defender has played just one game this season.
The club are unbeaten in the Premier League since the opening game of the season loss to Manchester United.
Much of that success has been down to the stability of the back-line which has been settled since the arrival of Toby Alderweireld from Atletico Madrid after his loan spell at Southampton came to an end.
He arrived from Sevilla last summer for a fee reported by The Sun but his career never truly took off, ever since seeing red on his debut against Manchester City back in October.
Fazio has struggled for game time this season. He has featured just once, in a Capital One Cup defeat to Arsenal, but was pictured training hard for this weekend's fixture - challenging with fellow misfit Kevin Wimmer.
Fazio is unlikely to feature v The Baggies this weekend and come January it would not be a surprise if he was granted a move elsewhere.