Sarabjit's lawyer Awais Shiekh told a news channel that Sarabjit's sister, Dalbir Kaur, had expressed the family's desire to return to India.
"After the doctors told her about Sarabjit's condition, she had first told me that they wanted to go back today. But later, in their hotel, they said that they will go back tomorrow," Shiekh told a news channel from Lahore.
Sarabjit Singh, 49, was admitted to a Lahore hospital in a critical condition after a vicious attack on him by fellow prisoners at the Kot Lakhpat jail April 26. He has been on ventilator support ever since.
His lawyer said that media had asked Dalbir Kaur if the doctors at Jinnah Hospital in Lahore had sought her permission to remove the ventilator support from Sarabjit.
India had Monday appealed to Pakistan for the release of Sarabjit Singh's release even as a medical panel in Pakistan said that he would continue to get treatment in Pakistan.
The ministry of external affairs in New Delhi had asked Pakistan to take a "sympathetic and humanitarian" view on Sarabjit.
Dalbir Kaur, Sarabjit's wife Sukhpreet Kaur and daughters Swapandeep and Poonam, had crossed from the Attari-Wagah border to Pakistan Sunday afternoon to visit him in hospital.
He has been on death row in Pakistan since 1990 after being convicted by Pakistani courts for bomb blasts in Lahore and Multan, which left 14 people dead.
Sarabjit's family claims he is innocent, and that he crossed over to Pakistan in August 1990 in an inebriated state and was arrested there.
Police in Pakistan, however, claimed that Sarabjit Singh, known as Manjit Singh, was involved in terrorist strikes.