The Baggies striker has been linked with moves to Celtic and Blackburn Rovers and head coach Steve Clarke has hinted that the Irishman could leave the club over the weekend
The Republic of Ireland international missed out on the Baggies' friendly with Barnsley on Saturday as the new boss feared his mind may be distracted by the offer.
Clarke hinted that the matter could be resolved one way or the other before the end of the weekend.
"A bid has been put in for Simon and you know what it's like when something like [this] happens," Clarke told West Brom's official website.
"The player can become a little bit distracted so I made the decision not to bring him today. Things might resolve themselves over the weekend. If they don't, Simon will be back working with us.
"In fact, I know he's due in tomorrow for training with the group."
Cox made 22 appearances in all competitions for the Baggies last season, but only 11 were starts. He scored four goals.