I have a looked at similar questions on this board, but none of them answer my question. This sound strange, but is it possible to mock out a constructor call on the object
And this is why you want to inject your dependencies (via Guice or similar package) instead of creating them inside your class.
Then you don't HAVE TO mock their construction.
This assumes (a) that this is your code that you can change, and (b) that the objects in question are complex enough that you should inject them. Constructing simple objects inside your class are fine, but then you shouldn't need to mock them.