It's rumored that Jungkook is dating ulzzang Park Sewon but no official statement is out yet. You can read more about it here: 

http://kpopkfans.blogspot.com/2014/02/bts-jungkooks-girlfriend-park-sewon.html 

Here is Park Sewon:

I will be happy for him whether he is dating her or not. I am sure that some fans will be throwing a fuss around but I think they have to keep in mind that he is a human and he has rights to love whoever he want and that he is 16, and that is probably considered the age for dating and such, he is still a teenager after all~

EDIT: Figured I should add this since many of the subscribers are saying that it is old. Yes, it is old but BigHit never said anything about this so up until now I don't think that fans should just jump into thoughts saying that they 'broke up' since we never knew if actuallt they were dating or not and if there 'were' dating we never know whether they brok up or not. Not to expand thissubject anymore I guess it's Jungkook's right to date her or break up with her. Whether this is old or new I believe we can never say anything about it until BigHit speaks out ^^