You might be aromantic.
Asexuality is a lack of desire for sex/lack of feeling of sexual attraction. You say you 'like men'. If you mean you want to have sex with men, then you're not asexual.
However, romantic orientation is separate from sexual orientation. Romantic desire is the desire to have someone as a life partner and form a long-term exclusive commitment to that person. While most people have matching romantic and sexual orientations and include sex as part of romance, there are romantic asexuals who want a romance without having sex, and there are also aromantic sexuals who want only sex and no relationship. People can also be heteroromantic, homoromantic or biromantic.
Romantic orientation isn't exactly analogous to sexual orientation, though, because it seems to me more malleable than sexual orientation. For example, I've encountered a number of gay guys who went through a phase of being heteroromantic homosexual, and as they got more comfortable with their sexual orientation, their romantic orientation shifted to match it. Also, avoidant attachment can make someone think they're aromantic when really they're repressing their desire for closeness. (The key distinction between aromantic and avoidantly attached is whether your aloofness extends to all close relationships, since romantic orientation has no effect on how you feel about your parents, siblings, children, friends, etc. An avoidantly attached person usually feels distant towards everyone, especially their own parents.)