Osaki loves Hachi?

It has been mentioned several times in the anime and manga that Nana loves Hachiko a lot.

Nana Osaki calls it desire. She thinks that she is a strange woman because she wants another woman all for herself. Even Yasu had pointed out in the anime that Nana tends to get very possessive. In fact, the padlock around Ren's neck is complete proof. She intends to keep him all to herself. Also, the tattoo she got of the Ren flower on her arm is yet another striking symptom.

Nana's possessiveness can get scary. She tells Nobu that she used him all along to keep Hachi in her own little garden, so that she won't lose her. The extent to which she goes is shocking.

But what Osaki doesnt realize is that it is completely natural for a woman as lonely as her to want friends and loved ones dearly. She knows their value, therefore she is possessive and afraid to lose them. It is also completely normal for her to want to keep Hachi all to herself. All she needs is a friend. And she found one.