The Brazil striker's time under Postecoglou has been marred by injury.
Postecoglou, on keeping Richarlison fit, said on Friday: “That’s a challenge. We’ve tried different ways, and Richy is trying different ways.
“We’ve been really careful in the way we’ve brought him back this time. He’s probably been ready to go for a couple of weeks. We’ve given him extra work.
“I thought he was really good when he came on the other night (at Arsenal), you could see his quality.
“He is one of these guys that does lead by example, particularly when he plays. It’s great to have him back.
“With Richy, it’s about him gaining confidence in his body as well. We can do that in the next few weeks.
“He’ll certainly play a part in the Everton game. Hopefully get him some more minutes than the other night, because if we can keep him fit, I’ve got no doubt he’ll be a really important player for us.”