Angelina Jolie has filed papers to adopt a child in Vietnam, the country's top adoption official said Friday.
According to the Associated Press, the director of Vietnam's International Adoption Agency said an American adoption agency representing Jolie had submitted the paperwork.
"She just filed the papers this week," Vu Duc Long said.
However, a source close to the actress tells PEOPLE, "The process began shortly after Shiloh was born."
The source adds: "It has been a long process and she is now simply waiting for further information."
Vietnam has one of the most complex and thorough processes in the world, the source explains, as a large number of reports must be created by Vietnamese authorities, background checks are undertaken, interviews are conducted and many meetings need to occur.
"That process could take a long time to unfold," says the source, "and while it is wonderful that people are excited about it, the news that papers have been filed is only the beginning of a very comprehensive and detailed process."
In addition to 9-month-old Shiloh, Jolie, 31, and Brad Pitt, 43, are parents to son Maddox, 5, and daughters Zahara, 2.
Jolie said in December
that she wanted more kids. "I'd like to add many more children and many more obstacles and many more things to my life," she told reporters while promoting her movie The Good Shepherd.
And Pitt told PEOPLE
in January that he and Jolie were hoping to expand their family. "Always, of course," he said. "We'll let you know when we get there."
The globe-trotting couple spent Thanksgiving in Vietnam
, taking a self-guided tour of Ho Chi Minh City, dining at a popular local restaurant converted from an old temple and later cruising around the former Saigon on a motorcycle.
Asked by a local newspaper how he felt about traveling the busy streets, Pitt replied, "There will be no problem," adding, "We had a wonderful day in Vietnam."
Jolie traveled to Vietnam
again in January for a meeting about the Maddox Jolie-Pitt Project, her charity aiding her son's native country of Cambodia.