The Liverpool head coach guided his team to seven points from three games in the division.
An away victory at Crystal Palace before the international break was followed by a home win over Chelsea and a 2-2 draw at Arsenal, where the Reds twice came from a goal down.
Slot is up against Nuno Espirito Santo (Nottingham Forest), Pep Guardiola (Manchester City) and Fabian Hurzeler (Brighton & Hove Albion).
Fans can vote for Slot to win here until 12pm GMT on Monday (November 4).
