Nothing is impossible, the worst thing the homeowner/landlord can say is no. With the rental market being as competitive as it is, do not expect to get much of a discount if it is priced fairly as the landlord will say he will just wait for a better offer, especially if recently listed. In the last year I have closed twice as many rentals as sales for the first time in my 9 year career and the most I was able to get discounted from asking was 12% and that was because it was overpriced, on the market for 3 months, and showed HORRIBLY due to mid-renovation. Luckily my clients saw the potential I pointed out and once it was completed it looked great. Best of luck in your search!