The 23-year-old former England Under-21 international striker, who has been heavily linked with a move away from The Hawthorns since summer 2015, has not played for the Baggies since the 1-0 defeat at Bournemouth on September 10.
Berahino was left out of the squad for Saturday's 1-1 draw against Tottenham on Saturday and reports have emerged that he was deemed to be carrying too much weight at tests prior to the international break.
It means he faces another spell out of boss Tony Pulis' plans with his contract due to expire at the end of this season.
Stoke City and Crystal Palace attempted to sign him in the summer and it is not known if they will follow up their interest in January in light of this news, while reports are claiming Berahino is pondering a move overseas and could sign a pre-contract agreement in January.
If he does move abroad then it will reduce the amount of compensation West Brom will be able to pick up for his signature.