Last week, Pakistan said it had offered to arrange a meeting between 46-year-old Jadhav and his wife, months after India had requested it to grant a visa to his mother on humanitarian grounds.
Foreign Office (FO) sources here said India in response has again asked Pakistan to issue a visa to Jadhav's mother so she can also visit her detained son.
FO spokesman Mohammad Faisal confirmed that India has responded to Pakistan's offer.
"Indian reply to Pakistan's humanitarian offer for Commander Jadhav received & is being considered," he tweeted.
Jadhav, a former Indian Navy officer, was sentenced to death by a Pakistani military court in April on charges of espionage and terrorism. The International Court of Justice (ICJ) in May halted his execution on India's appeal.
Pakistan has repeatedly denied India consular access to Jadhav on the ground that it was not applicable in cases related to spies.
Some media reports have linked Pakistan's latest offer to quiet efforts by the US. Pakistan, however, insisted that its offer was made purely on humanitarian grounds.
Jadhav has filed an appeal with Pakistan Army chief Gen Qamar Javed Bajwa to seek clemency, which is still pending.
Last month, the Pakistan Army had said it is close to a decision on the mercy petition of Jadhav.
Pakistan claims its security forces arrested him from restive Balochistan province on March 3 last year after he reportedly entered the country from Iran.
However, India maintains that Jadhav was kidnapped from Iran where he had business interests after retiring from the Indian Navy.
Jadhav's sentencing had evoked a sharp reaction in India.
After India approached the ICJ, a 10-member bench on May 18 restrained Pakistan from executing Jadhav till adjudication of the case.
The ICJ has asked Pakistan to submit its response or memorial by December 13 before the court could start further proceedings in the case.