Gibb, 62, has begun to show signs of recovery and has been able to nod and communicate with his family, spokesperson Doug Wright was quoted as saying by the BBC. Wright could not immediately be reached to confirm the report.
The singer contracted pneumonia and fell into a coma at a central London hospital earlier this month. He had been receiving treatment for colon and liver cancer.
He founded the Bee Gees with his twin brother Maurice and older brother Barry in the late 1950s. They have sold an estimated 200 million records during a career spanning more than 50 years.
The group helped to define the disco sound of the 1970s with a string of hits, including "Stayin' Alive", "Night Fever" and "Jive Talkin'". Their distinctive sound was characterised by falsetto vocals, tight harmonies and lush orchestration.