Nick Blackwell is no longer sedated after being operated on to reduce swelling on his brain.
Press Association Sport understands the retired middleweight is stable but as he is yet to wake his condition is being monitored.
The 26-year-old suffered the injury last Tuesday in an ill-advised sparring session that took place despite him no longer having a licence to box.
He had retired after collapsing at the end of his defeat by Chris Eubank Jnr in March, when he was found to have suffered a bleed on the skull and put into an induced coma.
While Blackwell remains in hospital and will continue to be monitored by doctors, the British Boxing Board of Control’s (BBBC) investigation into the circumstances surrounding his injury is also ongoing.
Their general secretary Robert Smith has spoken of their need to discover who oversaw the sparring session and who else was involved.
The incident happened without the knowledge of Blackwell’s former trainer Gary Lockett, who had encouraged the fighter to get his trainer’s licence if he wanted to remain in the sport.
Lockett said in a statement: “I can’t believe the boxer he sparred with, and (the) coach or coaches involved, would ever allow Nick to spar when he’s had a brain injury.
“In due course, I hope they are dealt with by the British Boxing Board of Control in the correct manner.
“We thought that was all going very well and while we knew Nick missed boxing, we obviously didn’t realise the extent to which he missed it.
“I am deeply saddened by what has happened. Nick is not just an ex-boxer of mine, but also someone I consider to be a friend.”