A man who fell from a hotel balcony with his two children will be arrested on suspicion of the murder of his son, a Foreign Office spokeswoman has said.
Mr Hogan was reported to have suffered chest, arm and leg injuries
John Hogan, 32, from Bradley Stoke near Bristol, will also be arrested for the attempted murder of his daughter once he has recovered from surgery.
Liam, six, died in the 50ft fall while daughter Mia, two, has been released from hospital with a broken arm.
The family of four were on a two-week holiday in Ierapetra, Crete.
A spokesperson for University General Hospital in Heraklion where Mr Hogan is being treated, said his condition was improving after he underwent surgery on a broken arm, leg and chest on Thursday.
"He is now breathing with a face mask and is awake and fully aware, and will soon be transferred to the orthopaedics ward," added the spokesperson.
He remains under police guard at the hospital.
Mr Hogan's wife, Natasha, works as a nurse in the accident and emergency department at the Royal Gwent Hospital in Newport, south Wales.
A statement from the family said they had not yet had an opportunity to talk to Mr Hogan about exactly what happened.
"All the family were looking forward to this holiday," the statement said.
"It was to be an opportunity for us to enjoy quality time together in an environment away from the general strains of daily life."
Liam's head teacher, Chris Dursley, of Wheatfield Primary School in Bradley Stoke, paid tribute to him saying he was a "delightful child".
"It's desperately sad that he should lose his life in such tragic circumstances," she added.
An assembly of remembrance will be held at the school when the new school term starts next month.