Template factory function with additional args: friendship issue

I'm working on a piece of code that looks like this:

template<typename T>
class A {
    // makeA should become a friend
    A() {}
};

template<typename T, typename U>
A<T> makeA(const U & u) {
    (void) u;
    return A<T>();
}

int main() {
    makeA<double>(3);
    return 0;
}

But I cannot let makeA become a friend of A. Is this possible? What is the right syntax?