Plans will be made to transfer jockey JT McNamara to the Mater Hospital in Dublin.
The 37-year-old amateur suffered a serious neck injury after a fall in the Fulke Walwyn Kim Muir Challenge Cup at the Cheltenham Festival and had to be airlifted to Bristol.
A statement issued on behalf of his family by Dr Adrian McGoldrick, Turf Club senior medical Officer, and Injured Jockeys Fund chief executive Lisa Hancock said: "JT McNamara remains in a stable condition at Frenchay Hospital, Bristol.
"He is now fully alert but requires full time ventilation at present. In due course JT will be transferred to the National Spinal Unit at The Mater Hospital where he will be closer to his family.
"His wife Caroline and family very much appreciate everyone's continued good wishes and prayers on JT's behalf."