The Manchester United hero's medical consultant said that the 59-year-old was "fighting for his life".
Former Northern Ireland forward Best has spent three weeks in intensive care in the private London Cromwell Hospital in west London after suffering an infection.
It was understood Best was on a life support machine and suffering from internal bleeding.
Considered by many as one of football's greatest-ever players, Best had a life-saving liver transplant in 2002 after decades of heavy drinking.
Alex Best said: "I have been told that George's condition has deteriorated dramatically during today (Wednesday).
"I am just praying that, once again, he somehow manages to pull through against all the odds. My thoughts and prayers are with him."
Professor Roger Williams, the consultant in charge of Best's care, told The Sun newspaper: "It may be an exaggeration to say that Mr Best is gravely ill. But he is certainly severely ill and is fighting for his life."
The professor told Britain's biggest-selling daily that he had not traced the cause of the bleeding.
He added: "We are not giving up. There's still a chance we can get him through this."