Sir Stirling Moss is said to be in a "stable" condition in hospital after being admitted with a serious chest infection last month.
The 87-year-old, who finished runner-up on four occasions in the F1 drivers' championship, was taken ill in Singapore on December 22.
Moss's family released a statement to announce that the motor racing legend's condition was continuing to improve after initially suffering complications from the infection.
"Because of the severity of the infection it resulted in some complications and his recovery has not been as speedy as was expected or wished," the statement read. "However, his condition continues to improve and his doctors now consider him to be stable. In himself, Sir Stirling is in good spirits and only upset about having missed his Christmas cruise with friends.
"The hospital in Singapore is second to none and the consultants, doctors, nurses, therapists and staff looking after him could not be more wonderful; as kind and caring as they are professional. Lady Moss says she could not wish for a better facility or a more qualified team. She is very grateful to them all.
"Once he is discharged from the hospital, it is Sir Stirling and Lady Moss's hope to stay in Singapore to enjoy a few days recuperating at a lovely hotel, being thoroughly spoilt, whilst lying in the sun by a gorgeous swimming pool. A little something to make up for the cruise they missed and with the bonus of escaping from the English winter for a while longer."
Moss, victorious in 16 of the 66 F1 races he competed in between 1951 and 1961, is widely considered to be one of the greatest drivers to never win the world title.