In response to Islamabad's offer earlier this month to allow the Indian spy to meet his wife, New Delhi requested that his mother be permitted to accompany her as well.
The Pakistan Army chief is now considering a Jadhav's mercy petition after his request for clemency was turned down by a military appellate court.
The offer was made on 10 November by the Pakistan foreign office through the Indian High Commission in Islamabad.
Islamabad last week took New Delhi by surprise by offering a meeting between Jadhav and his wife and it took a week for the latter to respond to the gesture, which Pakistan had said was on humanitarian grounds and as per "Islamic traditions and jurisprudence".
Pakistan has repeatedly denied India consular access to Jadhav on the ground that it was not applicable in cases related to spies.More news: Cool running of Nigerian Olympic bobsled team
Jhadav was arrested on March 3, 2016, in a combing operation against terrorists in Balochistan's Mashkel area. India has taken the Jadhav case to the International Court of Justice (ICJ).
Jadhav had confessed to the charges in a video which was posted online by Pakistan Army days after his arrest a year ago. However, the UN's top court on May 18 stopped Pakistan from executing the death penalty.
Pakistan had on Wednesday informed India that it would be willing to allow a meeting between the Kulbhushan Jadhav and his wife.
Pakistan's "humanitarian" offer had triggered tremendous speculation that the two countries could be moving towards some sort of understanding on the issue which in turn could see rock-bottom ties improving. Though diplomats on both sides are tight-lipped about the way ahead, unconfirmed reports have indicated that both sides have begun to discuss the modalities and venue of the meeting. A Pakistan spokesperson posted on Twitter that the response "is being considered".
On Saturday, Pakistan said it had received India's response and was considering the matter. He is also responsible for the murder of 1,345 innocent Pakistanis.