Pakistan's Ministry of Foreign Affairs said it has conveyed the decision to New Delhi and that the Indian reply is “awaited".
Indian sources said that Pakistani authorities have invited an Indian diplomat at 15:00 local time (Pakistan) to meet Jadhav. "One Pakistani official will also be present", sources added.
The consular access is being provided under the 1963 Vienna Convention; as per a demand put forth by the Indian External Affairs Ministry.
Meanwhile, the Indian Foreign Ministry said that it is currently evaluating the proposal and responding to Pakistan through diplomatic channels.
"We have received a proposal from Pakistan. We are evaluating the proposal in the light of the judgment of International Court of Justice. We will maintain communication with Pakistan in this matter through diplomatic channels", Raveesh Kumar, spokesperson for the Indian Foreign Ministry, said while briefing media in New Delhi.
The decision to allow consular access comes days after Pakistan authorities shifted Jadhav from a Lahore jail to an unidentified location outside the Lahore Central Jail.
On 25 July, Indian External Affairs Ministry’s spokesperson Raveesh Kumar said that it wants "full consular access" to Jadhav, 49, who was given the death sentence by a Pakistani military court on charges of "espionage and terrorism".
India, however, claims Jadhav is a former Indian Navy officer who was kidnapped and taken from Iran.
"We expect that full consular access to Kulbhushan Jadhav should be granted at the earliest in full compliance and conformity with International Court of Justice judgement and the Vienna Convention", Kumar said during a weekly briefing.
During the military court trial, Pakistan had did allow consular access to Jadhav to Indian authorities; due to which New Delhi approached the International Court of Justice (ICJ) last year.
On 17 July, the ICJ found Pakistan was "under obligation to cease internationally wrongful acts of a continuing character" for violating the 1963 Vienna Convention on Consular Relations.
The dispute over whether Pakistan will allow Indian officials to meet imprisoned Jadhav to converse in private, lies in the interpretation of the Vienna Convention, as it does not clearly spell out the nature of meetings.
Paragraph 2 of Article 36 of the Vienna Convention says: "The rights referred to in paragraph 1 of this Article shall be exercised in conformity with the laws and regulations of the receiving State, subject to the proviso, however, that the said laws and regulations must enable full effect to be given to the purposes for which the rights accorded under this article are intended".