Who asks someone to buy their dog?

So, there is this elderly lady that lives in the apartment below me who is CONSTANTLY asking me if she could buy my dog from me. You might say, oh I'm sure she's just joking, but I really think that she's serious...

To give you some back ground info. She lives by herself with an extremely annoying and aggressive small breed dog (I wanna say it's a Maltese). Anyway, she's always peeking out her window whenever we take him out and she either brings out her dog or comes out to talk. The problem is that her dog scares the crap out of Bandit because all he does is bark while tugging at his collar so hard that he is gagging. It's rather sad. Not to mention that she leaves her blinds open all day and lets the dog bark at anything and everything that walks by. ALL.DAY.LONG

One day I took the dog out and she is coming back from wherever and starts talking to me. Complimenting Bandit and saying how cute he is. Then she goes on to say how she wants another dog, she was thinking a Chihuahua. The whole time, I'm just thinking GREAT! now you'll have two dogs that bark all day. A few days later I see her again as I'm taking the dog out and she actually told me, "I would buy him from you but I don't think I can have another dog" I just told her that he wasn't for sale and just kind of laughed it off. Then, about 2 days ago she mentioned it again. Saying "If I had enough money, I would just buy him from you! Does he bark?" I, yet again, told her that he wasn't for sale. I mean SERIOUSLY! I already told you he wasn't for sale once, did you not get the hint? Not to mention, who sells their dog? AND... who sells it to someone that cannot even control the current dog they own.

I'm actually a little offended by her even thinking that I would be O.K selling him to someone. I think if she brings it up again I am going to tell her that I wish she would stop asking me if she could buy him. He's part of the family now and unless she was going to offer me an insane amount of money, it ain't gonna happen.