Television channel 9News saw Ingrid Alexandra at Sydney Airport and reports she is about to leave the country where she is studying.
The Norwegian Security Police (PST), which is responsible for the security of the royal family, declined to comment on the matter, NRK reports.
On Monday, Norway's Crown Prince Haakon told NRK that Ingrid Alexandra "plans to come home soon."
"It has to do with the family situation. She wants to be with her mother," said Haakon.
Haakon announced this weekend that a planned trip to Japan was cut short due to his wife Mette-Marit’s deteriorating health.
Mette-Marit has pulmonary fibrosis, which Haakon described last week as both serious and worsening.
