The Congolese midfielder has been at The Hawthorns since being snapped up from Paris St Germain in 2009.
The Baggies have helped the 26-year-old to raise his profile, and he admits he owes the club 'a lot'.
Mulumbu has, however, aired a desire to step up to the next level and secure a switch to a side that is regularly competing in Europe.
"I have been at West Brom for almost five years. They are a family club, with good spirit," Mulumbu told France Football.
"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."