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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.