Boxer Nick Blackwell remains in an induced coma but could be brought round very soon, a spokesman for his family has said.
Blackwell collapsed shortly after losing his British middleweight title in a bout against Chris Eubank Jr at Wembley’s SSE arena on Saturday night.
The fight was stopped in the 10th round due to swelling above his left eye. Minutes later Blackwell was carried from the ring on a stretcher while being given oxygen. He was later diagnosed with a bleed on the brain and placed in an induced coma.
A spokesman for his family told the BBC his condition was “not deteriorating” and raised the prospect that he could be brought out of the coma on Tuesday.
On Monday his family thanked the public for their messages of support and called for privacy during the difficult time.
Eubank's father, Chris Eubank Sr, a former world champion, said on Tuesday that he and his son's primary concern was for Blackwell's health.
Eubank Sr, who was in his son's corner for the bout, was involved in a world title fight with Michael Watson in 1991, which left his opponent with severe brain injuries and led to improvements in safety at fights.
But some have argued that the referee, Victor Loughlin, should have stopped the largely one-sided fight sooner, despite there being no knockdowns, due to the level of punishment Blackwell was taking.
Peter Hamlyn, a leading neurosurgeon who operated five times on Watson, told the Guardian that the title bout should have been stopped in the seventh round as Blackwell had received "dozens and dozens" of "neuro-physically significant punches" in the fight while landing only two in return.
Eubank Jr landed a number of uppercuts during the fight which repeatedly jolted Blackwell’s head backwards. Hamlyn added that he felt for the referee. “It is very tough to be in the ring under all that pressure trying to make instantaneous decisions,” he said.
Robert Smith, the general secretary of the British Board of Boxing Control, has defended Loughlin's decision to let the fight continue as long as it did.
A crowdfunding page set up on Monday to support "warrior Nick Blackwell" by fellow British boxer Adam Etches had raised almost £4,000 (€5,000) by Tuesday morning.
A number of British boxers, past and present, including current heavyweight champion Tyson Fury and former champion Lennox Lewis, have posted messages of support for Blackwell on social media.