I used to eat with my mouth opened. This habit was changed by my colleague and I am sharing what she did which really worked. And I wonder if she checked this link for this.
First of all, don't tell it loudly and in front of everybody else because this might make that person feel hatred for you. If you really need to tell that while you're eating in a group, try telling him/her in a voice lower enough to let him/her hear.
Now, you can tell him/her like this.
I'm sure that you don'tdo not realize it, but you're chewingyou are eating with your mouth open. (Source)
or
I'm sorry, but it's kind of difficult for me to eat while seeing someone eating with their mouth open. Can you please not keep your mouth opened while eating?
Now, you've got to repeat it as long as it is necessary since it does not usually take too many attempts before he/she realizes that he/she is eating with opened mouth.