Efforts to find the family began in August after India accepted the woman, named Geeta, was one of its citizens.
Geeta, who has speech and hearing impairments, was about 11 when she is believed to have strayed into Pakistan.
Her plight emerged following a Bollywood film Bajrangi Bhaijaan, which told the story of a Pakistani girl who cannot speak and is trapped in India.
For most of her time in Pakistan, Geeta has lived at an Edhi shelter home in Karachi, reports the BBC's Shahzeb Jillani. Staff at the charity gave her her name - she is now thought to be about 22.
"The Indian high commissioner has lately sent a family photo to us and Geeta has recognised the family," Anwer Kazmi, a senior official at the foundation, told AFP news agency.
"We have showed the picture to Geeta and she says they are her family... We hope she will confirm the family identification during the Skype chat through sign language."
Geeta was unable to provide a name, address or any documentation to the Pakistani border guards who found her over a decade ago. Nor could she explain how she ended up across the border.
Once her travel documents are sorted, she could leave for India as early as 26 October, Faisal Edhi, the son of Pakistan's leading charity worker Abdul Sattar Edhi, said on Thursday.
The Edhi Foundation was trying to arrange a Skype call between Geeta and her family, who live in the Indian state of Bihar, he added.
It was not clear when the Skype chat would be held.
Although it was long thought that Geeta was Indian, it was only in August that the authorities in Delhi accepted her as a citizen - and said she would be brought back home soon.
Foreign Minister Sushma Swaraj said then that she would be handed over to her family after a DNA test.
An Indian woman stranded in Pakistan for a decade has identified her family in photos sent from across the border.