She said in the last few days, four families from Punjab, Bihar, Jharkhand and Uttar Pradesh have claimed Gita, who is in Karachi, to be their daughter.
"We are completing the necessary formalities to bring Gita back to India," Swaraj said in a tweet adding "I am requesting the Chief Ministers of these states to verify and report."
Indian High Commissioner in Pakistan TCA Raghavan and his wife on Tuesday had met Gita following a direction from Swaraj and assured her of locating her family as soon as possible.
"She also conveyed that she had visited a temple with her father. Then she wrote down 'Vaishno Devi'," Swaraj said.
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The External Affairs Minister also retweeted a drawing posted on tweeter by one Yusra Askari with a caption "Geeta's drawing of home - number 193, that as per her is located near a fish pond, paddy fields and a maternity home."
"This should further help in locating Gita's family," Swaraj said.
Gita, 23, is believed to have mistakenly crossed into Pakistani territory as a child. She was 7-8 years old when she was found by the Pakistan Rangers 15 years ago from Lahore railway station, according to reports from Pakistan.
Gita's story found way to media after the Salman starer blockbuster.
Pakistan's human rights activist Ansar Burney had also raised Gita's ordeal.