For one thing, Samuel Nuuyoma, the governor of the Namibian province where Pitt, 42, Jolie, 30, and kids Maddox, 4, and Zahara, 1, are staying, will not be visiting the hospital and naming the new arrival, despite tabloid reports.
Britain's Daily Mirror had quoted Nuuyoma as saying, "When she goes to the hospital, as the father of the region, I will be informed and I will go there. I will announce the good news and I will be naming the baby."
But Nuuyoma, who has met the couple, told the Associated Press on Wednesday, "No. No. That's absolutely not true. I never said such a thing. Never in history."
However, no official government action seems to have taken place.
One thing, however, is certain: Foreign journalists wishing to cover the birth must have written permission from Pitt and Jolie to enter the country and obtain a work permit, the Namibian government has said.
The order follows the arrest of John Liebenberg, a South African magazine photographer, who was apprehended Wednesday for the second time in less than a week while trying to take pictures of the couple at a restaurant, according to the South African Press Association.
The Jolie-Pitt family arrived in the sleepy coastal town of Walvis Bay last month and have been shielded by their own bodyguards and Namibian police at a luxury resort hotel.
The impending birth of their first biological child prevented Pitt from joining costars Cate Blanchett and Gael Garcia Bernal and director Alejandro González Iñárritu at the Cannes Film Festival on Tuesday to promote the new movie Babel.
Instead, he sent his regrets in an e-mail, saying, "With the imminent arrival of the newest addition to our family, I am unable to join Alejandro, Cate, Gael and the rest of the cast and crew introducing the film."
Reporting from Cannes, PEOPLE movie critic Leah Rozen calls Babel "an accomplished piece of filmmaking (and) a favorite to take home the festival's top prize Sunday."