As reported by The Guardian's Barry Glendenning, the Congolese international has attracted attention from Arsene Wenger following a stellar 2012/13 campaign followed by an impressive start to this term.
The former Paris Saint-Germain player was given an opportunity at the Hawthorns after the Ligue 1 side had deemed him surplus to requirements and now face losing him to a side that can offer European football.
It appears that Mulumbu's head has been turned amid the speculation, with Glendenning reporting the midfielder as saying:
I have had approaches from Arsenal. I could leave this winter. This is the right time for me to set my sights higher.
I'm ready to join a top four club. We are not professional enough in the way we manage our games – for example our draw at Chelsea. We are not mature enough.
West Brom manager Steve Clarke will surely not be too impressed with his player's comments. However, the Baggies have had to deal with want-away players in the past—Peter Odemwingie a prime example—and will not be held to ransom because of Mulumbu's outburst.