The petition filed by the couple is likely to come up before a bench for hearing on Thursday.
The couple had been sentenced to life imprisonment by a special CBI court at Ghaziabad on November 26, 2013.
Aarushi was found dead, with her throat slit, inside the Talwars' Noida residence in May, 2008. Hemraj, who had gone missing, was initially suspected of being involved in the crime until his body was recovered from the terrace a day later.
The sensational case was handed over to the CBI following outrage over the handling of the matter by the Uttar Pradesh police.
The trial court had pronounced its judgement accepting the probe agency's submission that the couple had killed Aarushi and Hemraj in a fit of rage after finding them in an "objectionable position".
With PTI inputs