Is there such a thing as craving for enlightenment and would it be unwholesome?

I was wondering if for example an obsession or craving that someone has for attaining Nirvana would be considered something unwholesome. On one hand it seems to me like it would, since that person would be reinforcing the habit of craving, but on the other hand how else could they actually achieve the goal? Like for example how could they decide to become a monk and devote themselves fully to the practice etc. I don't think the Buddha would have left his palace if he wasn't motivated by *some* sort of craving, at least in the beginning.