You cannot do that, because of 2 reasons.
- It doesn't make sense.
- The factory that should instantiate the object will throw a "circular dependency" exception.
I'll start with the second point.
If you do it like that, when you try to instantiate your helper, the dependency injection container (DIC) will look for an instance of your class to pass it to your class constructor.
But that class instance does not exist, so DIC will try to instantiate it and you are back at the previous step.
And here is why it doesn't make sense.
You would need a dependency on your class because you need to call a method from that dependency, but you can already call methods from your class inside your class. You don't need an other instance to call methods from that.