It's only possible if you modify some game files. The only official romance options for Male Shepard are Ashley and Liara. Kaidan becomes a romance option in ME3, however.
Mark Meer, the voice of Male Shepard, recorded all of Female Shepard's unique lines to make sure they wouldn't miss anything, but the Kaidan romance dialogue was not meant to be in the game. It is, however, still in the game files, which means you can unlock it through some tweaking: http://social.bioware.com/1517619/blog/47401
Keep in mind that this is unofficial and won't carry over into Mass Effect 2.
