Mulumbu arrived at the Hawthorns in 2009 and has made 155 Premier League appearances for the club.
The Congolese midfielder has a contract until the end of the season, but has indicated he is ready to leave if the right offer comes in.
He said in The Sun: "I have been at West Brom for almost five years. They are a family club, with good spirit.
"But I spoke to the coach and the director of football and they know my ambitions for the future.
"If I get the chance to join a more classy club, I will do so.
"I owe West Brom a lot. But I have now reached a level where I can go somewhere else and play in the Europa League or Champions League."
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