According to the Mirror, the boy was a pupil at Harryville Primary School, who released a statement this evening.
"The five-year-old boy fell into the water at around 1pm today".
The family also thanked the emergency services for their efforts in the search, which included police, firefighters, the Northern Ireland Ambulance Service (NIAS) and Community Rescue Service volunteers.
Mr Swann added: "In the midst of this bad tragedy, I also commend all the efforts of the emergency services, air ambulance crew, police and hospital staff".
The child was then flown to Royal Belfast Hospital for Sick Children, where he died of his injuries sustained.
In a statement on Facebook, the school said it was "a very sad time".
Earlier:A boy was swept more than four miles down a fast-flowing river in Antrim before being pulled out by rescue teams.
He was dragged out more than 45 minutes later near Tullaghgarley and airlifted to hospital.
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An NIAS spokesman said they despatched the air ambulance, an A&E crew and a doctor to the scene.
He said: 'He got swept away quite fast with it, he was travelling quite a distance.
TUV leader Jim Allister, who like Mr Swann is an MLA for North Antrim, said: "My heart goes out to the local family in Ballymena who lost their young boy in Saturday's river tragedy".
Mr McCarry said rescuers were "running desperately" after the boy, while a police helicopter watched from above.
"The thoughts of all involved in the rescue are with the young boy and his family".
At approximately 15.04pm, the child was found and pulled out of the river.
The youngster spent more than 45 minutes in the water and travelled a minimum of four miles down the river, Mr McCarry said.