A bench of Justice Siddharth Mridul issued notice and sought response from Neelam Katara, mother of Nitish Katara on the plea moved by Yadav.
The bench posted the matter for further hearing on February 23.
In his plea, Yadav said he needed parole for two weeks to sell his ancestral property in Uttar Pradesh to file appeal against his conviction and sentence in the case.
The high court had on February 6, 2015 enhanced the sentence of Vikas and his cousin Vishal from life imprisonment to 25 years without remission for murdering Nitish Katara and five more years for destruction of evidence in the case.
Yadavs' acquaintance Sukhdev Yadav alias Pehelwan was also awarded an enhanced life sentence of 20 years without remission by the high court.
The three were awarded life term by a trial court for abducting and killing Katara, a business executive and son of an IAS officer, on the intervening night of February 16-17, 2002. They did not approve of the victim's affair with Bharti, daughter of D P Yadav.
