Official sources said Shinde has given time to the family, including Sarbjit's sister Dalbir, to hear their grievances.
The family, which crossed over to India after visiting 49-year-old Sarabjit, said his life can be saved if the Indian government puts pressure on Pakistan to shift him to this country or abroad for better treatment.
The family is expected to meet Prime Minister Manmohan Singh, UPA Chairperson Sonia Gandhi, External Affairs Minister Salman Khurshid besides Shinde to urge them to help save Sarabjit's life by taking necessary steps.