Best Approach to Offer Buying From Your Landlord?

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I'm considering offering to buy our rental from our landlord because she's about to raise our rent higher again, which we can't afford.  It's a dump, so there's room to fix it up for equity, too.  

Dear Landlords: Any advice on the best approach for this? It needs a lot of work, so I would of course ask for a discounted price, but I've been concerned it will offend her, or plant the idea to list publicly on the MLS and put us out of a place to live (since there's plenty of people who can overbid us these days). Thoughts?