It isn't currently possible. In the current implementation users with view permissions on the page can post and users with edit permissions can moderate/edit or delete any post.

I've added a wish list item for this in our project tracker but not sure if/when we would implement it. If we did implement it, it seems it could be confusing. An unauthenticated user would see the prompt that you must sign in to post in the forums and then they sign in and still can't post would be frustrating. So we would need to think through how to present these messages to avoid frustration. Implementing the permission requirement would not be technically difficult, figuring out how to keep it friendly is the trickier part. I guess making it possible to edit those messages is what would be required but we would need to come up with some good default text for those scenarios.

Best,

Joe