Alongside Jake Livermore, Jayson Molumby and Alex Mowatt, Snodgrass is one of just four central midfielders in the Baggies squad.
But the former Scotland international hasn’t made the bench for Albion’s last three games.
Boss Valerien Ismael has confirmed Snodgrass is not injured.
But he has refused to give to give any more details about the 34-year-old’s absence.
Asked on Friday why Snodgrass hasn’t been involved, Ismael said: “I picked the squad, as usual. I take the decision, the final decision, and this is the situation at the minute.
“There is nothing more to say about the situation.”
It us understood, Snodgrass has now been told he is free to leave the club in January.
It remains to be seen if he’ll be involved at Coventry on Saturday – with both Livermore and Molumby suspended.
Speaking earlier this month, Snodgrass said he was hoping to play a big part for the Baggies this season.
The midfielder struggled with a back injury last season which ultimately required surgery.
That operation ensured Snodgrass wasn’t fully fit for the start of the current campaign.
But he made his first league start of the season in the win over Bristol City last month and responded with a man of the match display.
“I want to play my part in getting it back to where it belongs (Premier League) this year because it’s a great club,” he said.
“I’m as hungry as ever and that’s why I’ve done months of rehab.
“Getting my first start in seven or eight months was a great feeling.
“I want to kick on and the more minutes I get, the better I’ll become.”