Pakistan had first offered the consular access to Jadhav in August but India had insisted that the consular access should be 'effective and unhindered.'
India has maintained that Kulbhushan Jadhav was kidnapped from the Iranian port of Chabahar where he was running a business.
Earlier this month, Jadhav, who has been detained in Pakistan since 2016, had met Charge d'Affaires at the Indian High Commission in Islamabad, on consular access granted by Pakistan.
The meeting came a month after a similar interaction between Indian officials and Jadhav did not materialise amid differences between New Delhi and Islamabad.
Charge d' Affaires at the Indian High Commission in Islamabad Gaurav Ahluwalia will meet Jadhav, the sources said.
Pakistan's response came after India, on August 29, had asked for "immediate, effective and unhindered" consular access to the former navy officer.
In July, the Hague-based ICJ ordered Pakistan to grant India consular access to Jadhav without further delay.
ICJ ordered Pakistan to undertake an 'effective review and reconsideration' of the conviction and sentence of Jadhav and also to grant consular access to India.
Salve, is the lawyer who defended India at the International Court of Justice in the Kulbhushan Jadhav case and had charged only Re 1 from the government.
On July 17, the ICJ ordered Pakistan to undertake an 'effective review and reconsideration' of the conviction and sentence of Jadhav and also to grant consular access to India without further delay.
On Thursday, India sent a communication to Pakistan making clear its position that the consular access must be "unimpeded" and should be in the light of the ICJ judgement.
India, on Thursday, had said that the proposal sent by Pakistan to grant consular access to the Indian national was being evaluated as per the guidelines provided by the International Court of Justice
Pakistan offers consular access to Kulbhushan Jadhav on Friday, India says 'will reply through diplomatic channels'
UN court had ordered Islamabad to make an "effective review and reconsideration" of his conviction and death sentence and also grant consular access.
Jadhav, 49, a retired Indian Navy officer, was sentenced to death by a Pakistani military court on charges of "espionage and terrorism" in April 2017 following which India had moved the ICJ.
In a reprieve for Jadhav, a 16-member bench of the International Court of Justice on July 17 held that Islamabad violated New Delhi's rights to consular visits after his arrest.