Some villains have asked me about relations with their heroes - sexual attraction, interest in them as a friend, or whatever. Usually this comes down to "how do I turn my hero into a villain like me?"
This is usually the wrong question to ask. Flip that shit around and ask yourself: "under what circumstances would I stop being a villain and start being a hero?"
In lucha libre, the tecnicos and rudos are the good guy and bad guy wrestlers. American professional wrestling has "face" and "heel" for good and bad guys. The trap you might be falling into is identifying too closely with "good guy" and "bad guy" here, because that "face" and "heel" opposition is basically just a marketing gimmick devised by wrestling promoters. Any time there's a "good" and "bad" side, "good" is expected to win because that's how society rolls. But villains aren't necessarily "bad". We do our own thing, for our own reason. You have to remember that heroes are the same way. They hunt villains and stop crime not because they're some sort of innately moral, virtuous people, but for as many different motives as we have.
The question you should be asking, instead, is: "is the hero-villain dynamic going to stand in the way of what we want?" The answer, generally, is: not unless you've made the conflict personal. And sometimes you can even get around that.
What do I mean by personal? Kidnapping family or friends. Death threats to loved ones. Bombed homes or the workplace of a secret identity. Outing each other's secret identity. That sort of shit. If that's the level you took it to, do not expect to be on cordial terms any time soon.
That said: there's plenty of times when the good looking villain is giving the D to the attractive heroine, and I don't mean the Death ray. I know of heroes and villains who meet for coffee - each pretending not to know who the other is. There are some who are bitter rivals in costume and good friends in their civilian identities.
Your challenges in building this sort of relationship are finding out if your nemesis is interested, and broaching the subject. Supers, as a rule, feel a certain alienation from mundanes. We can do things they can't, and vice versa. We share more with each other, despite our moral views, than we'll share with mundane allies of our particular viewpoints. This means that once you form such a relationship, it will probably be self-sustaining, provided neither of you throw a monkey wrench into it. Well, at that point, you guys were nemeses already, so it's back to business as usual.
Is your nemesis interested?
This is hard to gauge. You have to separate your own feelings about the matter from what you're getting from your hero. The easiest way to do this is to ask a few trusted friends if they see anything between you. Maybe your hero hesitates before attacking. Maybe he or she has let you off the hook more than other villains. Maybe he or she seems more receptive to your dialogues during a caper. That sort of thing.
A sub-issue is: does your nemesis want the same thing you do? Maybe you're an attractive female villain and really just want someone to talk shop with, and your male hero seems most likely to understand you, but when he gets home at night, all he can think about is your ass. This is not really going to work out, because he'll misinterpret your interest, and you will probably misinterpret his.
How do you broach the subject?
Assuming you have some confidence that your hero is interested, you should express interest of your own subtly, in stages. Get a little flirtier. Point out the couples at the coffee shop. Say things like "only you understand me." Put out those careful feelers.
You'll know if your hero is interested if he or she keeps up with your signs of interest. Whatever signals you're giving off, expect to see some of the same kind coming back from the hero. Again, feedback from a trusted source is really helpful here.
Never, ever trust the newspapers to accurately report what's going on here, by the way. "Sparks fly between dueling superhumans" is a story intended to sell papers, not describe reality. Magazines like "People", "Secret", and "Masked" routinely run stories insinuating non-existent relationships. A few years ago I was being linked romantically with Titania. I want nothing to do with that woman, and the fact that we're both size-shifters and "that means something" is bullshit.
So in conclusion - get a wingman or best girlfriend. Work out what you want, look for signs of interest, and gradually float trial balloons. Maybe it'll work out, and maybe not. You're not getting any younger, but you are getting older at a dramatically slower rate, so don't worry! You have time.