Gibb, 62, diagnosed with cancer of the colon and liver, contracted pneumonia and became comatose in a hospital in Chelsea, west London, last week but has shown signs of recovery, Britain's The Daily Telegraph reported.
Gibb has been able to nod and communicate with his wife Dwina, daughter Melissa, 37, and sons Spencer, 39, and Robin-John, 29, spokesman Doug Wright said.
Gibb's twin brother and bandmate Maurice died from the same bowel condition that initially led doctors to operate on Robin 18 months ago, a procedure that led to the discovery of cancer.
It had been believed his cancer was in remission last month, but his health has deteriorated and there have been reports of a secondary tumor.
Gibb last performed in February at the London Palladium in a charity concert for injured servicemen and women.