He and a girl that was a spy infilterating Konaha actually kissed in one of the fillers. What happened was, after she was interrogated by the ANBU he was supposed to be watching her. Naruto and some friends followed them around setting traps so that he would kiss her or get to know her better. At the end of the filler, Kakashi was supposed to kill her but she thanks him for everything he did for her and he hesitates. He put away his kunai and told her to leave and make sure that she didn't come back. So basically it's the closest thing to a girlfriend we've seen him have in the series.