Tima Kurdi, who lives in Canada, told broadcaster CBC that Alan's uncle and his family would be granted asylum.
Canadian officials would only confirm that their application was proceeding.
Three-year-old Alan died along with his brother, five, and his mother trying to reach the Greek island of Kos.
Images of Alan's body on a beach near Bodrum in September caused an outpouring of sympathy for those fleeing to Europe to escape Syria's civil war.
Tima Kurdi told CBC that approval of an application for Alan's uncle Mohammed, his aunt Ghousoun and their five children had been confirmed in an email from Immigration Canada earlier this month.
"It will happen. They will bring them," Ms Kurdi told CBC from her home near Vancouver.
A spokesman for Immigration Canada, Remi Lariviere, would not give details of the case but added: "We can confirm that the processing of their application is proceeding well."
Following Alan's death, Ms Kurdi said Canada had rejected his family's request for refugee status, but later acknowledged it had never been submitted.
Hundreds of asylum seekers have died this year trying to reach Europe by sea and Turkey has become a major transit point.
On Friday, Turkish media said six children had drowned when two migrant boats carrying them from Turkey to Greece sank in the Aegean Sea.
The first boat carrying about 55 mainly Syrian and Afghan migrants sank off the Turkish town of Ayvacik in bad weather.
On Saturday, the EU is due to finalise a plan with Turkey that could see Ankara given both financial aid and visa-free travel for its nationals in return for more action on refugees.
Members of the family of Syrian boy Alan Kurdi, whose drowning off the coast of Turkey triggered an international outcry, are to be admitted to Canada, his aunt says.