The Swede arrived at The Hawthorns last summer from Werder Bremen but has made only five starts in all competitions and is yet to score a goal for the Baggies.
The form of Shane Long and Romelu Lukaku has been the main barrier to Rosenberg, while Peter Odemwingie is also ahead of him in the pecking order despite his disciplinary issues.
Clarke told the club's official website: "Markus is very disappointed things haven't worked out for him so far. He hasn't had enough minutes on the pitch.
"Some of that can be my fault and he can be unhappy with me. He shouldn't be unhappy with himself. He trains every day, he's a consummate professional and he is well liked in the group.
"It's been a disappointing season for him. But there are still eight games to go and there is a little bit of me hoping in those eight games Markus gets the chance to play and shows everyone what he can do."