Long has been left out by Ireland boss Giovanni Trapattoni for the friendly international with Greece on November 14 amid concerns over a hamstring problem.
But Clarke insists Albion have been managing the condition effectively in recent weeks and is convinced Trapattoni will change his mind should Long face the Saints.
He said: "With Shane, we've been managing things for a little while. 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.
"He joined in training today and fingers crossed he will be okay for Monday."
Clarke added: "Ireland haven't picked him but I'm sure if he plays for us on Monday night, they can change their squad.
"I've got no idea if they will. I can't worry myself about what the Irish FA are going to do with their squad.
"We've a duty to get the players on the pitch for West Brom. That's what we try to do.
"Shane has had this issue for a couple of weeks now, I think we've managed it really well.
"It hasn't affected his performances in anyway whatsoever and that's what we will try to do going into the future.
"The Irish game is not until the middle of November. We've got two games before that. I have to think about those two games."
But Clarke will be happy if Trapattoni has a change of heart regarding Long.
He said: "If he goes with Ireland, I'll be delighted. I've never stopped a player from going to play for their country. It is a fantastic honour.
"It's one regret I've got from my career, that I never played enough for Scotland, and I would never stop anyone from playing for their country."
Albion skipper Chris Brunt and right-back Billy Jones are back in contention to face the Saints after a three-game absence with hamstring and knee injuries respectively.