The Liverpool boss – winner of the prize in August, September, November and December so far this season – led his side to five successive victories.
Sheffield United, Tottenham Hotspur, Manchester United, Wolverhampton Wanderers and West Ham United were beaten as the Reds stretched their lead at the top to 19 points.
Klopp is up against Pep Guardiola (Manchester City), Ralph Hasenhuttl (Southampton) and Nigel Pearson (Watford) for the January accolade.
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