Both strikers have been forced to the sidelines this season due to injury, with Solanke currently facing a fresh spell out.
Asked about Richarlison's fitness, Postecoglou said: "As fit as he could possibly be. We are obviously managing his minutes at the moment. He got through it last night. He hasn’t played for a long time so he is not going to be his sharpest. We have still got to manage that. The reality is, unless something changes, he has to play.
"I don’t think Richy cares about Dom Solanke or anybody else. When Richy is playing he is Brazil’s No 9. When he played for us last year he was scoring goals. I don’t think Richy was ever worried.
"I think he will welcome Dom coming back. Both of them playing together could be a force for us. I don’t think that factors into it. Richy is just happy he is physically in good shape and able to start contributing and a lot of the injured guys their biggest probably frustration is that they can’t help the team. I know that is his main driver right now."