Yes, that is what prefetch_related() is for. It will require an additional query, but the idea is that it will get all of the related information at once, instead of once per Person.
In your case:
qs.select_related('position__report_to')
.prefetch_related('position__report_to__person_set')
should require two queries, regardless of the number of Persons in the original query set.
Compare this example from the documentation:
>>> Restaurant.objects.select_related('best_pizza')
.prefetch_related('best_pizza__toppings')