I don’t run without my pup though
I think that Dany is attracted to Jon because she thinks he's 'special' like her. Now this doesn't mean they're kindred spirits or anything. Rather, in her narcissistic mind, he's like a male version of herself: young, attractive, great leader, white savior, fierce warrior, special snowflake (lol). Of course, I don't think that she's truly interested in having a man or children anymore? I think those dreams died with Drogo and her son. That's why she won't want to share the throne with Jon.