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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.