The Liverpool manager, who won the accolade for August, guided his team to top-flight victories over Newcastle United, Chelsea and Sheffield United last month.
Those results saw the Reds maintain their 100 per cent winning start to the Premier League season and open up a five-point lead at the top of the table.
Klopp is up against Eddie Howe (Bournemouth), Frank Lampard (Chelsea) and Brendan Rodgers (Leicester City) for the September prize.
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