The amateur rider fractured two vertebrae in his neck during a fall last Wednesday and had to have surgery on his broken neck.
However, the rider's family have released a statement saying that no brain injuries have been detected and that while he remains in an induced coma, the level of sedation is being reduced.
"His wife Caroline and family very much appreciate all the messages, cards and letters that have been received," the statement continued.
"There will be no further update this week."
The 37-year-old was riding Galaxy Rock for trainer Jonjo O'Neill in the Fulke Walwyn Kim Muir Challenge Cup on Wednesday when the pair fell at the first fence.
An air ambulance landed at the racecourse to treat the injured rider, who was conscious after the fall but had difficulty breathing, and he was taken to the hospital.
- Sports & Recreation