The Sunday Mirror reports that Arsenal boss Arsene Wenger had the midfielder watched at Stoke a week ago.
Wenger is looking to strengthen his squad in January in order to to maintain a challenge at the top oft he Premier League.
Mulumbu signed a new contract at West Brom in the summer and the Baggies are keen to keep the Democratic Republic of Congo international at the club.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?