Salah has received his second POTM nomination in a row after scoring in each of his three league appearances for the Reds, netting five goals in total.
The Egyptian attacker began the month of October by scoring a brace in a 2-2 draw at Brighton & Hove Albion, before netting both goals in Liverpool's 2-0 home triumph over Merseyside rivals Everton.
Salah then found the net in a 3-0 win against Nottingham Forest last weekend, increasing his goal tally in this season's Premier League to eight in 10 games and helping Jurgen Klopp's side climb into the top four.
Meanwhile, Arsenal's record signing Rice is in contention to win his first-ever divisional award having been recognised for his influential displays in midfield, playing in all but one minute of the Gunners' three top-flight games in October.
The England international played a key role in Arsenal's narrow 1-0 home victory over reigning Premier League champions Manchester City, before scoring a stunning long-range goal to help Mikel Arteta's side rescue a 2-2 draw at London rivals Chelsea.
Rice then provided an assist for the opening goal scored by hat-trick hero Eddie Nketiah in Arsenal's thumping 5-0 win over Sheffield United at the Emirates Stadium last weekend.
Another midfielder who enjoyed an impressive spell in October was Aston Villa's Douglas Luiz, who has received a monthly nomination after contributing with two goals and one assist to help Unai Emery's men claim seven points across three Premier League matches.
The Brazilian netted twice in Villa's 4-1 win over West Ham United, becoming the first Lions player to score in six
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