The 61-year-old, who was admitted to hospital in May, is receiving 24-hour care but does not have coronavirus.
Sansom, who won 86 caps for England and played 394 games for Arsenal, has had well-publicised problems with alcoholism and gambling.
A tweet read: "Kenny remains ill in hospital and is receiving 24-hour care. He's stable and does not have COVID-19.
"Kenny's family and close friends still kindly ask the media to respect Kenny's privacy and theirs, plus that of the healthcare workers treating Kenny."