Korean call that kind of man "아싸" "아싸"is short for "아웃싸이더" "아웃싸이더" is phonetic Korean for "outsider" As you know it is diffrent between loner and outsider but "아싸" is Konglish. So I think best suitable expression for "loner" is "아싸" or "아웃싸이더" As above "mynick" said, "혼자 있기를 좋아하는 사람" or "고독을 즐기는 사람" will be correct also.

IMO, there seems be no exactly matching word in Korean. I thought about "외톨이" or "왕따" but these words indicate those who are left out by others. So, if I translate a loner into Korean, it should be a little lengthy wording, "혼자 있기를 좋아하는 사람" or "고독을 즐기는 사람".