What's the English equivalent of "闺蜜" 闺蜜 in Chinese means two girls have very good relationship, and much closer than normal good friends but they are not lesbians. 

The best I can get is the term intimate relationship, but it could be used to describe lesbians. Any other good suggestions?
Preferred translation:
Bestie
New Century English-Chinese Dictionary
Defines Bestie as:

挚友；好哥们儿；闺蜜；死党

Urban Dictionary #1 def:

A person who means the world to you. The person that when you met you just kinda connected. The person that you were always there for. The person that isn't a love partner but they hold a special place in your heart. Someone that when they get hurt it hurts you too. Someone who no matter what happens between you two everything always ends up being alright. A person you can trust with anything.
Richie is her bestie. She is his bestie. They are forever besties no matter what.

and definition #2

An adoring nickname for one you hold in highest esteem, more commonly known as a best friend. A bestie is the person who you not only go shopping with on a regular basis but also trust implicitly with anything.. besties do not come and go like waves and sandcastles, they are more like permanent marker on American Eagle jeans, they'll stay with you forever. It is much better to have one pure andgood bestie who is true to you then multiple 'besties' (even though if theres more than one t usually will not count as a bestie, technically) who are only like pants that stay with you only until you get too fat for them, or you tear them (like hurting them, and then them being all unforgiving), or just until they fade. A true bestie would stick with you through all of it, walking in when the world walks out.
Boyfriend: Hey, wanna go to the movies with me later?
You: Oh my gosh I'm sorry maybe tomorrow I've got plans with my bestie already. I would never blow her off!


An alternative:
Bosom Buddy

Noun
bosom buddy (plural bosom buddies)
A very close friend.