Arsenal are believed to be among those chasing the 26-year-old midfielder, who has excelled at The Hawthorns since arriving from Paris Saint-Germain in 2009.
"[West Brom] are aware of my ambitions for the future," he told France Football. "If I have the opportunity to join a more upscale club, I will.
"I owe West Brom a lot but now I would only go elsewhere to play in the Europa League or Champions League. I think it is the right time. I have progressed in my game, my game management, mentally, tactically, physically and I am ready to go to a top-four club.
"There have been approaches, but I do not dwell on it - I leave it for the club and my agent to handle. England is my first destination. I feel good here, there is no longer a language barrier. Beyond that, maybe there are opportunities with other clubs in the Champions League."
Mulumbu has won 20 caps for the Republic of Congo.