Her relatives and supporters have offered $1m (£735,000) as diyah, or blood money, to be paid to Mahdi's family.
"We are still trying to save her. But ultimately the family has to agree for pardon," Babu John, social activist and member of the Save Nimisha Priya Council, told the BBC last week after the date for her execution was set.
The Indian foreign ministry sources said on Tuesday that its officials had been in touch regularly with jail authorities and the prosecutor's office in Yemen, where there has been a civil war since 2011.
The government "made concerted efforts in recent days to seek more time for the family of Ms Nimisha Priya to reach a mutually agreeable solution with the other party", they said.
Nimisha Priya left Kerala for Yemen in 2008 to work as a nurse.
She was arrested in 2017 after Mahdi's body was discovered. The 34-year-old is presently lodged in the central jail in Sanaa, the Yemeni capital.
In 2020, a local court sentenced her to death. Her family challenged the decision in Yemen's Supreme Court, but their appeal was rejected in 2023.
In early January, Mahdi al-Mashat, president of the rebel Houthis' Supreme Political Council, approved her execution.
Yemen's Islamic judicial system, known as Sharia, offers her one last hope - securing a pardon from the victim's family by paying blood money to them.
Nimisha's mother, a poor domestic helper from Kerala, has been in Yemen since April 2024 in a last-ditch effort to save her.
She has nominated Samuel Jerome, a Yemen-based social worker, to negotiate with Mahdi's family.
A lobby group called Save Nimisha Priya International Action Council has been raising money by crowdfunding for the purpose and Mr Jerome has said that $1m has been offered to Mahdi's family.
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