Partially default initialize template template parameters with internal type

Partially default initialize template template parameters with internal type

template <template <typename> class container_type>
class MyClass
{
class Internal{
};
};
I want to use this class (or how it would look correctly) in a way like
the following...
MyClass(std::list);
...so that in MyClass container_type is declared/typedef'd as:
std::list<Internal*>
Is something like this somehow possible?