The Tottenham defender had looked set to make a reported £5 million switch to the Hawthorns.
The defender had looked like moving to the Hawthorns from White Hart Lane after Tony Pulis earlier confirmed that the player was at the club for talks and a medical ahead of a transfer.
Sky Sports now say that the deal is off, and West Brom are already pursuing alternative options at the back.
The Argentine only joined from Sevilla last summer, but suffered a disappointing season in North London, going on to make limited appearances especially in the Premier League.
A concern for Spurs fans will be that the collapse of the deal will have implications for their chase of Baggies star striker Saido Berahino, but there is no indication that the failure to secure Fazio's signature has anything to do with the clubs, or the England Under-21 forward. It has been reported that West Brom and the giant Argentina international were unable to agree terms despite Fazio having passed a medical this morning.
Jonny Evans could be an alternative says a separate report, after the Manchester United veteran was closely linked to a move following a flood of bets on a Baggies switch, although Sky Sports do suggest that Fazio could yet make the move on loan before the transfer window shuts.