Extending Static Inner Class Defined Within Inheriting Class?

I am working on a project involving a class that has the attributes of one of its inner classes. Now, if possible, I would like to make it so that the inner class is not visible outside of the class. Also, some of the functional mechanics require that the class be an instance of the nested inner class (it extends the inner class). The following code snippet demonstrates the situation.

public class A extends A.B {
public static class B { //ideally I would like this to be private/protected.
}
}

When I try to compile this program, I get the error message "Cyclical inheritance involving A." This error does not make much sense because, since the inner class "B" is static, it requires no instance of "A" (it does not inherit from "A" or uses it). My question is "Is it possible to do something similar to this structure?" I have searched many forums in search of the answer but have not found anything that attempts to explain it. The closest problem that I have found is one relating to the inheritance of a nested inner class from another class. I would like to express that the problem that I am having involves a class defined within the inheriting class.