The couple, who have been dating for less than a year, want to "ensure real privacy" for their baby and will keep him or her off of the Kardashian family's reality show and its various spinoffs, the celebrity news website said.
Although no birth special is planned, Kardashian will share her remaining six months or so of pregnancy with TV viewers, TMZ said.
West announced at a New Jersey concert during the weekend that Kardashian is pregnant with their first child. Her famous family later confirmed she is about 12 weeks pregnant.
Celebrity Breakups and divorces of 2014 [PHOTOS]