You can ask any friend to be your roommate (but not an acquaintance),provided they are not in a relationship with someone (gf/bf, fiance, spouse). As far as i can tell, you can't ask a pregnant sim, or any sim who lives with a child or baby/toddler, even if there may be other adult sims in their household to look after them.
You need to have sufficient roommate allowance: if your sim is living by themselves, enable roomate service and set it to the appropriate number of roommates so that you can ask an additional sim to be roommate.
Remember that rm will start showing up at 9 am the day after, so if you set it up in the evening, and then go out and ask a friend to be rm the next day, make sure no NPC sim has already arrived at your house, in which case you will be able to ask your friend, but they won't, in effect, be able to BE your rm, even if they accept.
If you can't ask a sim to be rm, it is probably that you haven't enabled the appropriate number of rm, or that they are in a relationship with another sim that you don't know of.