The former champion boxer shot in the head after asking three men to stop smoking is still in a critical condition in hospital, police said.
James Oyebola, 47, had previously stunned doctors by responding to tests, it was reported, but he was said to be still fighting for his life.
It was thought early on that the former British heavyweight champion may be brain damaged after being shot at close range in a London nightclub in the early hours of Monday morning.
According to The Sun, consultants said just one side of Mr Oyebola's brain was affected, raising hopes that he may survive without brain damage, and doctors treating Mr Oyebola at the High Dependency Unit of Charing Cross Hospital were said to have reported nerve movement after performing a tracheotomy to help him breathe.
But police on Thursday confirmed that he was in a fight for survival.
Mr Oyebola's solicitor, Scott Ewing, said the family had been encouraged by the results of the tests.
The 6ft 9ins former champion was shot in the head and leg in a covered courtyard area at the rear of Chateau 6 in Fulham Road, west London. Four shots were fired but no weapon has been found.
Mr Oyebola, known as Big Bad during his fighting career, arrived at Chateau 6 at about 11pm on Sunday for a drink with the owner after finishing work at a nearby bar.
He was shot shortly before 1am after intervening to help staff who had asked three men to stub out their cigarettes.
His attackers, described as black and aged between 19 and 25, fled the club on foot - apparently in separate directions.
