The 59-year-old former footballer began to breathe for himself as medical staff at the private Cromwell Hospital in west London turned his ventilator down and he showed he was aware of his surroundings.
Professor Roger Williams, who oversaw Best's liver transplant in 2002, said he was still in a serious condition with internal bleeding and kidney problems but there was "an increasing degree of hope".
He said: "He's recognising people. He's better in that respect but please don't run away with thinking he's fantastic because there's still a long way to go. He has not spoken."
Professor Williams said medication for the internal bleeding seemed to be working but there was much to do to get all his organs functioning. The main worry was Best's kidneys which were "affected by the bleeding and the infections".
Best would remain in intensive care for the next few days, he said. " It's the long haul when somebody has been as ill as this."
Professor Williams added that he should suffer no "long-term harm from these acute episodes" and should get back a very reasonable quality of life.
Phil Hughes, Mr Best's close friend and agent said: "I started to talk to him and he gripped my hand. He's unable to talk as yet but he's certainly aware when we are talking to him.
"There's no doubt that he is still seriously ill but little signs like that are enough to say he's on the mend."
Doctors said Best's transplanted liver was functioning well, despite his acknowledged alcoholism. He has been treated for an infection for the past four weeks, to which he is especially susceptible as a result of the immunosuppressant drugs he takes to prevent his liver being rejected, and his condition deteriorated severely earlier last week.Reuse content