The Ukraine international was granted a day off last week following Russia’s invasion of his home country. The 32-year-old returned to training this week but was left behind in London when West Ham traveled to Southampton on Wednesday night.
While Moyes is unwilling to pressure the winger to return, the manager will assess Yarmolenko on Friday before deciding if he is ready to return to the squad at Anfield.
“He’s been training, hopefully he can come back,” Moyes told Standard Sport.
“I don’t think physically is the biggest problem, but I think mentally we might have to give him a few days. But I will assess him on Friday.
“He trained again on Thursday. When we went to Southampton he trained at the training ground on Wednesday so he had a few days to recover.
“But again, mentally we just have to make sure. I don’t feel like I want to push him, I want him to tell me when he’s getting closer to being ready.”
Former Ukraine international Andriy Shevchenko claimed on Wednesday night that Yarmolenko had traveled to Poland to meet his family, although West Ham and Moyes both denied the story.
“It wasn’t right, no,” Moyes said.
Moyes will also have to assess the fitness of Aaron Cresswell who missed the trip to Southampton through injury.