The Latics are in desperate need for points as they battle against relegation from the Premier League.
Meanwhile, the Baggies are safely in the top half of the Premier League with four games remaining, although they find themselves six points behind seventh-placed Liverpool.
There is a six-point gap between Clarke's men and Swansea City, but the Scot said that his team are still sharp despite all but guaranteeing eighth place.
"I don't think [Wigan] will get an easy game here," Sky Sports News quotes Clarke as saying. "Not too many teams come to The Hawthorns and get an easy game, and I don't think that will be the case this weekend.
"Maybe Southampton thought last week that it was a mid-table clash with nothing on it. We certainly went down there and showed them it mattered to us and that we wanted the points.
"It's no different this time. We have our own ambitions and our own targets. We like to finish the season well and play well in front of our own fans. The game against us, I can assure you, will be difficult, because we've been good at home."
Roberto Martinez's men are five points adrift of safety.