Whenever you download media by own, it will be stored under the Phone's Gallery. This is due to Media Visibility is enable by default. Keep a note the feature only implies to new media that's downloaded once the feature has been enabled or disabled and doesn't apply to older photos and videos. To Stop From All Individual Chats And Groups From Being Saved: Head to WhatsApp > More > Settings. Tap on Chats and then disable Media Visibility. To Stop Media From A Particular Individual Chat Or Group: On WhatsApp, open the chat of individual or group. Select More, and hit the Group Subject or Contacts. Up next, select Media Visibility > No. And then OK.