I am considering relocating to another state and the company I work for doesn't offer a relocation package. Is it ok to ask for a week's pay or a stipend? It will take me three days to drive there and then find an apartment.
Companies will generally consider relocation assistance when the need arises from some action the company takes. For example, I have received relocation assistance twice in my career, the first when I was newly hired for a job in a different state and the second when my company physically moved its office location. A responsible company will provide assistance when your need to move is because of them.
You say you are "considering" relocating, which makes me think this is for your benefit or desire, and not the company's. If this is the case, I don't feel this a time you should be asking for assistance from the company. They should not be financially responsible for supporting your choice to change where you live.
If you want to relocate: you pay
If the company wants you to relocate: the company pays
If it's beneficial for both you and the company: negotiate