People with pets tend to treat them, and feel, as if they're members of their family. It may be killing the original owner that they had to give up the cat (I've had to do the same thing temporarily while I lived in a "no pets" motel, while looking for a place - first thing I did once I got a place was drive the 500 mi to get my cat back). You can ask the original owner if they still want the cat. If they do, I would suggest going online after you get your own place, and visit nokill shelter sites. There are plenty of cats in need of good homes, my current cat spent its first 5 years of life in a cage at the shelter.
Some places will offer an adoption discount if you take a "senior" resident or a cat with special needs.