The 25-year-old was dropped from Giovanni Trapattoni's latest Republic of Ireland squad for their friendly against Greece on November 14 due to a knee injury.
"With Shane, we've been managing things for a little while," said Clarke. "It's an unfortunate situation because the Irish want to name their squad two weeks before [the game].
"For us, we are doing with Shane what we've done over the last two or three weeks. We are managing him between games. We are trying to get him fit for Monday night."
The Baggies currently sit eighth in the league table.