The brothers' mother, identified as Rihan, is believed to have drowned alongside her children. Their father, named as Abdullah, survived. The family were from the Kurdish town of Kobani.
Speaking to the National Post, Teema Kurdi, Abdullah's sister who has lived in Vancouver, Canada, for over 20 years, said she heard the news through a phone call with the wife of another brother, Mohammad.
"She had got a call from Abdullah, and all he said was, 'My wife and two boys are dead,'" she said.
According to another local Canadian report, the Kurdi family were trying to come to Canada, but had their G5 visa application rejected in June. Teema and her friends had attempted to sponsor them, but were denied "owing to the complexities" of Turkish applications.
On Thursday, the Canadian government denied they had received a refugee application from the family.
Aylan, 3, was pictured lying lifeless on the beach in red shorts, a T-shirt, and trainers. In a second photo, he is seen being carried away by a Turkish police officer.
The boys were believed to have been trying to cross the Mediterranean on two boats with other Syrian-Kurd refugees.
The refugees were attempting to reach the Greek island of Kos on Wednesday morning, according to the Turkish coastguard.
They were travelling on two boats when one of the boats, carrying six people, capsized, according to a local Turkish report. The BBC reported that, of the 23 people on board the two boats, only nine are thought to have survived. Several people wearing life jackets managed to swim to the shore.
The Kurdi family were fleeing Kobani, a Syrian city engulfed in a civil war that has displaced about 4 million people, according to the UN Refugee Agency.
Abdullah Kurdi said he plans to take the bodies of his two children and his wife, Rihan, home to Kobani, Syria.
Kurdi told the AP: "I tried to catch my children and wife by there was no hope. One by one they died. My kids were the most beautiful children in the world, wonderful, they wake me up every morning to play with them. They are all gone now"
The father of two told the AP that the boat, heading towards the Greek island of Kos, lost control after the captain panicked due to the high waves and jumped into the sea. Abdullah was left to take control of the boat. He said the boat was only at sea for four minutes before the captain abandoned the craft.
"I took over and started steering. The waves were so high and the boat flipped. I took my wife and my kids in my arms and I realized they were all dead," he said.
"I just want to see my children for the last time and stay forever with them," he said.