The south coast club sit third in the Premier League table behind Chelsea and Manchester City with seven matches played.
Koeman, who was up against Crystal Palace's Neil Warnock, Jose Mourinho of Chelsea and Leicester City's Nigel Pearson for the award, guided Saints to three wins in the Premier League during the month as well as a Capital One (League) Cup win over Arsenal at the Emirates stadium.
His side beat Newcastle 4-0 and Queens Park Rangers 2-1 at St Mary's, while also picking up the points with a 1-0 win at Swansea City.
Pelle, who scored on his international debut for Italy this week, also scored twice in the win over Newcastle and hit a spectacular overhead winner against QPR.
Southampton's French midfielder Morgan Schneiderlin was also nominated for the player's award.
(Reporting by Mike Collett; Editing by Amlan Chakraborty)
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