"They won't be shipping his remains back for a couple of days because of formalities," Gladys told the New York Post.
Gladys said she is not surprised, adding, "Listen, I lived there for five years — nothing is done quickly."
According to his mother, Bourdain's estranged second wife, Ottavia Busia Bourdain, is still legally Bourdain's next of kin.
"Although they're separated, she'll be in charge of whatever happens," the mom said. "We haven't talked for a couple days. I'm sure she's as broken up as I am."
Bourdain and Busia were on good terms at the time of his death, although they split in 2016. The couple shared custody of their 11-year-old daughter, Ariane, who lives in New York with her mother.
Gladys said they want to have the body flown back to the U.S. for the funeral, but the plans are ultimately up to Busia.
A source who worked closely with Bourdain told PEOPLE magazine Friday that the Kitchen Confidential author was on a grueling work schedule in the weeks before his death.
"His travel schedule was grueling and he often seemed quite beat-up from it, as anyone would be," the source told the magazine. "He'd put everything into the shoots and then go back to his room to isolate."
The source said it appeared Bourdain "gave everything to his work and then had nothing, zero, left for himself afterwards."
"He was always very, very tried," the source said. "He pushed himself extremely hard. Most producers and crew don't work on every single episode, it's just too much especially if you have a family. But that wasn't an option for Tony. We never had any sense of depression or mental illness. He was not especially cheerful or engaging, off camera, but it was never rude or ill-intentioned. The guy was absolutely exhausted."
Bourdain openly discussed his personal demons and struggles with depression. In his 2010 memoir, Medium Raw, he wrote about feeling "aimless and regularly suicidal" after the 20-year marriage to his first wife, Nancy Pitoski, ended in 2005.
The 61-year-old Bourdain was found dead Friday after he took his own life at the Le Chambard hotel in Kaysersberg-Vignoble, France. He was filming a new episode of CNN's Anthony Bourdain: Parts Unknown with his friend, chef Eric Ripert, who found the body.
If you or someone you know needs help, please call the National Suicide Prevention Lifeline at 1-800-273-TALK (8255).