Pakistani diplomatic sources said they were "positively considering" India's request to repatriate him.
"We are positively considering the Indian request to repatriate Sarabjit Singh to India," a diplomatic source told PTI. The sources did not give any other details and it was not clear when a decision on the issue would be made by the Pakistani government.
The move came hours after New Delhi announced that Indian High Commissioner Sharat Sabharwal had sought the immediate release of Sarabjit during a meeting with Pakistan foreign secretary Jalil Abbas Jilani.
The request for releasing 49-year-old Sarabjit - comatose since Friday after he was attacked by other prisoners in Kot Lakhpat Jail - was conveyed by Sabharwal during the meeting held yesterday.
Ministry of external affairs sources said in New Delhi that Pakistan has agreed to India's request for consular access once a day to Sarabjit.
In New Delhi, an external affairs ministry spokesperson said, India was "concerned at the condition of Sarabjit Singh indicated by reports made available by doctors treating him in Jinnah Hospital" in Lahore.
The Indian High Commissioner had met Pakistan's foreign secretary and urged the Pakistan government to "immediately release (Sarabjit) on humanitarian and sympathetic grounds so that he can benefit from the best available treatment in India", the spokesperson said.
India has alternatively proposed that Sarabjit could be sent to a third country for proper medical treatment.
"This is not the time for invoking legal and bureaucratic reasons for not taking the right steps to save a human life. We believe that every endeavour should be made to save his life," the spokesperson said.
Speaking to reporters in Gurgaon, external affairs minister Salman Khurshid said he was sad over the health condition of Sarabjit. He added that India has sent a proposal to Pakistan and it is now upto Pakistani government and doctors to decide.
Earlier, official sources in Lahore said Sarabjit had slipped into a "non-reversible" coma and this could lead to "brain death".
His measurements on the Glasgow Coma Scale, which indicates the levels of consciousness and damage to a person's central nervous system, had dropped to a "critical level", the sources said.
A source said Sarabjit's heart is beating "but without brain function" because of the extensive head injuries he sustained when he was assaulted on Friday. Sarabjit is completely unresponsive and unable to breathe without ventilator support.
The sources said the medical board supervising Sarabjit's treatment was not in a position to declare him brain dead without consulting his family and Pakistani authorities. The sources further said Sarabjit could not be removed from the ventilator without his family's consent and the approval of the Pakistani government.
Sarabjit's wife Sukhpreet Kaur, daughters Poonam and Swapandeep Kaur and sister Dalbir Kaur, who went to Lahore on Tuesday to see him, returned to India this morning.
Yesterday, doctors treating Sarabjit at the state-run Jinnah Hospital said his condition had further deteriorated though he had not been declared brain dead. They said his blood pressure was being maintained with support and his chances of survival were very slim.
Sarabjit sustained several injuries, including a fractured skull, when six prisoners attacked him in jail on Friday afternoon. He was hit on the head with bricks and has been comatose in hospital since then.
He was convicted of alleged involvement in a string of bomb attacks in Punjab province that killed 14 people in 1990. His mercy petitions were rejected by the courts and former President Pervez Musharraf.
The previous Pakistan Peoples Party-led government put off Sarabjit's execution for an indefinite period in 2008.
Sarabjit's family says he is the victim of mistaken identity and had inadvertently strayed across the border in an inebriated state.