India had moved the Hague-based International Court of Justice (ICJ) against Mr Jadhav's death penalty handed down by a Pakistani military court. The ICJ had on May 18 restrained Pakistan from executing the death sentence.
Pakistan government's functionaries have started consultations for the nomination of an ad-hoc judge, Express Tribune reported, citing sources.
During the tenure of ousted Pakistani Prime Minister Nawaz Sharif, former Supreme Court judge Khalilur Rehman Ramday was approached, but he declined the nomination, the report said.
Sources were quoted by the daily as saying that the Attorney General for Pakistan's (AGP) office has recommended the names of senior lawyer Makhdoom Ali Khan and former Jordanian prime minister Awn Shawkat Al-Khasawneh to the Prime Minister's Office for the nomination of one name as an ad-hoc judge.
Mr Khasawneh served as an ICJ judge for over a decade, while Mr Khan, a former Attorney General who is seen as the favourite for the job, also has experience in international arbitration cases, having represented eight different countries in international courts.
The nomination of the ad-hoc judge will be finalised after getting inputs from the Foreign Office and the military establishment, the sources said, adding that earlier, government functionaries had also considered the name of former chief justice of Pakistan Tassaduq Hussain Jillani.
An official was quoted as saying that the name of the ad-hoc judge will be finalised next month, soon after the Indian side files its documents.
Meanwhile, Pakistan Bar Council (PBC) representative Raheel Kamran Sheikh has called upon the government to seek Parliament's approval on the appointment of the ad-hoc judge.
Only one person has previously been appointed as ICJ judge in Pakistan's history -- former foreign minister Zafarullah Khan, who was appointed in 1954 and later became the president of the court.
Yaqub Ali Khan and Sharifuddin Pirzada both served as ad-hoc judges, as did Zafarullah Khan.