Reports claim the young boy woke up earlier than his parents and wandered from their hotel room.
He is believed to have jumped into the pool at the Atlantica Holiday Village resort on Saturday morning.
Local reports say his devastated parents found him in the pool and dragged him out.
The little boy, who was given CPR, is understood to have died before emergency services arrived at the scene.
It is believed he was on holiday with his parents, siblings and extended family and was part of a group of ten, who had been on Kos island since Wednesday.
A Foreign and Commonwealth Office official said: "We are supporting the family of a British child who died in Kos, Greece, and our staff are in touch with the local authorities."