Zouma found himself at the centre of a storm over the mistreatment of his pet cat, and withdrew from the team to face Leicester last weekend after feeling unwell during warm-up.
Asked if Zouma was in contention to face the Magpies Moyes said: "Well, he's better, but it's taken him a couple of days to get over it.
"He had quite bad sickness and illness, but he's trained the last couple of days, so I'm hoping that he'll be available."
Asked how Zouma was mentally, Moyes added: "I think he's probably really disappointed about what he's done and he's thinking about it a lot, no doubt, but overall we have tried to get him to move on.
"We want him to concentrate on his training. He played very well for us against Watford the other week there, so we're hoping that we can keep him at those levels of performance - we'll be pleased with that.
"He's really well-liked here amongst the supporters, the performances he's put in throughout the season already, so hopefully he can focus on his football and we'll give him as much support as we can until we get him right back to his best."