I identify as asexual. I don't want sex either. I've done some reading on it, and I found out there are people who are asexual but are romantic. (There are also those who are asexual and aromantic. I assume sexual and aromantic is also possible) They want a romantic relationship, just not a sexual.
I think what you mean by friendship is a platonic relationship. There's a difference between platonic and romantic. Not sure what it is.. but I think platonic is wanting to be together and romantic being happy staring into each other's eyes for hours or something?

By the way - I prefer to say "I identify as asexual" rather than "I am asexual" because really, how can I know what I am? Maybe it will come some day (I'm 20 now, but it's known people with autism sometimes enter adolescence later than those without autism), maybe I'm not biologically asexual but just traumatized, maybe it's because I got physically sick at 12 and by the time I got better (after my leg amputation age 15) I was suffering from depression, severe PTSD and taking a lot of medications (first for the physical, now for the mental) and I just haven't had time to busy myself with that yet? Who knows. So I just say, "I identify as asexual". And if in ten years I feel differently, I'll say "I identify as sexual" or homosexual or heterosexual or bisexual or ..

By the way, AVEN - the Asexuality Visuality and Education Network - says that you can be asexual at one point and then ten year later be some-kind-of-sexual.
They also say asexuality is a spectrum - ranging from people with very limited sexual interest, gray-asexuals, demisexuals (the latter need an emotional connection before they can become physically attracted), and people with no sexual interest at all. There's asexuals who masturbate and those who don't. There's asexuals who think sex is OK as long as they don't have to do it, and there's asexuals who think sex is icky. Asexuals who use toys, those who use porn, those who use both, those who use none.
It's a spectrum.

I'm not saying you are asexual or are on the spectrum, just saying you might find some information on relationships between asexuals useful, or relationships between an asexual and a sexual person.

AVEN has a lot of information. In particular, here's a "Relationship FAQ" about having a relationship when one or both is asexual:
Relationship FAQ | The Asexual Visibility and Education Network | asexuality.org