Mulumbu has established himself as one of the best defensive midfielders in the Premier League since joining West Brom initially on loan in 2009 before making the move permanent.
The 27-year-old was one of West Brom's shining lights in a disappointing campaign last term and a number of clubs across Europe are thought to be monitoring his situation at The Hawthorns.
Mulumbu has never hidden his ambitions to play at the highest level possible and the DR Congo international is thought to have admirers among top clubs in the Premier League, Serie A and Bundesliga.
The player's agent, Doug Pingisi, has admitted the former Paris Saint-Germain man is keen to test himself at the highest level and would find it hard to turn down the chance to play for a club competing in Europe.
"Youssouf has completed a good, consistent season despite the difficulties West Brom encountered," Pingisi told Sky Sports.
"He's demonstrated that he's gone up a level and has matured all round. He's now aspiring to test himself in European competitions."