I understand the importance of monitoring your Voice Mailbox. Though the App directly on the phone does not offer notification you will be notified if calling Voice Mail directly by dialing *86 that your box is full. The max number of Voice Mails that you can store is 40 Messages.
Follow us on TWITTER @VZWSupport
If my response answered your question please click the _Correct Answer_ button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!!