It's the landlord's responsibility. I would say if they're trying to sell, they won't want a rat/mouse problem! Ring the real estate.

I hear what I think is a possum thumping around in our roof ocassionally.. not sure it lives there tho, coz it's pretty infrequent. Could it be possums? They have a pretty horrid shriek sometimes.

Either way, I'd report it to the real estate. Potential buyers will probably send through pest inspectors too.. so just mention it to them!