What's holding you back? Why don't you begin a conversation? I'm quite sure if you're qualified, you shall be the first in line. Please act as if you're unaware of his/her financial situation. Some like to keep their situations private.
You can start by discussing with the landlord your interest in possibly purchasing the property--if the landlord agrees to the sale, make sure you are aware of recently closed similar properties in the immediate area in order to establish a fair offer--don't forget to visit with any qualified loan officer(s) as well if a loan is needed; see exactly what your budget can handle and what mortgage product will suit your needs. Any local agent and or an attorney who specializes in real estate can help you with all related paperwork.