The centre-back helped the Reds keep two clean sheets in their two league games during April and weighed in with a headed goal herself in the 2-0 win against Lewes Women.
Moore, 24, is now firmly established at the heart of an LFC Women defence that conceded just 15 league goals all season – the joint-lowest in the division.
The New Zealander is hoping to follow in the footsteps of her captain Niamh Fahey, who was named the Player of the Month for March.
It would also bring up a superb treble, with midfielder Ceri Holland scooping the league award for February.
Also nominated this month are Katy Morris (Coventry United), Jess King (Charlton Athletic) and Tatiana Saunders (Lewes).
The winner will be decided by a combination of a 48-hour public vote and an expert panel.