Clarke admitted for the first time that the Sweden international could leave after just a year with the Baggies after failing to make an impact in the Premier League.
The 30-year-old has started just two league and three cup matches since his free-transfer switch from Werder Bremen and was without a goal ahead of today's Hawthorns meeting with Arsenal.
Asked whether Rosenberg could look to move on, Clarke said: "That's not a discussion we've had yet but I'm sure that between now and the start of next season we will sit down and discuss it because he's not a young man anymore. He's not the type of lad who is happy to just sit on the bench and pick up his money.
"I'm sure we will sit down and discuss what is the best thing for Markus and the best thing for Albion."
Rosenberg has found his first-team chances limited by the form of leading scorer Romelu Lukaku and Ireland international Shane Long. And Clarke admitted a lack of match action had not helped the former Ajax man's cause.
"The minutes he's had on the pitch probably haven't been enough," said Clarke.
"He can be disappointed with me but he shouldn't be disappointed in himself because he puts in a good shift every day in training and he is the consummate professional – always trying and working at his game.
"It's been a frustrating season for him and he's never really been given the chance to show his true potential."