Professor Roger Williams, who performed a controversial liver transplant for Best in 2002, said he expected him to remain in intensive care for another four to five days.
Best, 59, is still breathing through a ventilator, but by last night the internal bleeding had almost stopped. Professor Williams said his patient had had "a series of infections", but added: "On the whole there has been a very definite improvement in his condition but he is still requiring a lot of care."
The player's condition remained serious, Professor Williams said. However, the transplanted liver was holding together well, and doctors had been able to reduce the amount of antibiotics given to Best since Thursday. He will remain under sedation until tomorrow.
Best was admitted to the private Cromwell Hospital in west London on 2 October suffering from an infection caused by immunosuppressant drugs he has been taking following his liver transplant. The drugs stop his body rejecting the new liver, but they also increase the risk of infection and can cause septicaemia.
As well as being attached to a ventilator, Best has a central line inserted into a large vein in his neck through which as many as five tubes will run.
Other drips, giving the patient fluid, painkillers and drugs to maintain the liver transplant, are also attached.
He is also thought to have a tube though his nose into his stomach. This is known as a nasogastric tube, which allows doctors to feed a patient and give drugs that would normally be taken orally. Best has an ECG to monitor his heart rate, a pulseoximeter a small clip on his finger measuring his pulse, and an arterial line in his wrist to measure his heart rate and to take blood tests.
Arguably the greatest footballer of his generation, Best had a dazzling but brief career at Manchester United. He took a leading role in the club's 1968 European Cup victory and was named European footballer of the Year. In the 466 matches he played for the club, he scored 179 goals.
With his extravagant skill, easy charm and good looks he became the first celebrity footballer and was dubbed the "fifth Beatle". But his high-profile social life and heavy drinking became legendary, as did his penchant for going out with Miss Worlds.
His United career ended in 1974 when he was finally sacked after failing to turn up for training.
The alcoholism that ruined his football career has continued throughout his later life. In 2000 his doctor, Professor Williams, warned Best that one more drink would kill him, and in April 2001 anti-alcohol pellets were sewn into his stomach. Despite this, and a life-saving liver transplant operation in July 2002, he carried on drinking. Best's nine-year marriage to his wife, Alex, hit the rocks not long afterwards.
Best famously said of his lifestyle: "I spent a lot of money on booze, birds and fast cars. The rest I just squandered."