Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The Swedish international has struggled to make an impact since his move from Werder Bremen to the Baggies last summer and has started just two league matches.
"It's been a frustrating season for Markus. He's never really been given the chance to show his potential mainly down to the form of the other players," Clarke said.
"I'm aware Markus is really disappointed, and a little bit down. He comes to speak to me quite often. I respect him for that. He lets me know his frustrations face to face.
"Does he stay beyond this season? That is not a discussion we've had yet. I'm sure between now and next season we have to sit down and discuss things because he is not a young man anymore.
"He is not the type of person who is happy to sit on the bench and just pick up his money. I'm sure it's a conversation we will have.
"We will sit down and decide what is the best thing for Markus and West Brom."
Rosenberg has been behind Shane Long, Romelu Lukaku and Peter Odemwingie in the pecking order this season.