The couple's appeal against the High Court order was mentioned before a bench comprising justices BS Chauhan and Dipak Misra which posted the matter for hearing on May 28.
This the second time this month that they have knocked the doors of the apex court with the plea to summon additional witnesses, including ADG (Law and Order) Uttar Pradesh and then CBI Joint Director Arun Kumar to record their statements.
They have challenged the dismissal of their petition by High Court's May 21 order which had said: "There is no need to force the prosecution to call witnesses other than those it deems proper."
The High Court was of the view that the trial court had the right to decide which of the witnesses should be summoned and their statements recorded.
The couple had moved the High Court after the apex court on May 13 had refused to entertain their petition after taking strong exception to Talwars directly challenging the trial court's order before it.
The apex court bench had asked them to approach the High Court saying it was a wrong procedure to approach the Supreme Court directly.
While the Talwars are seeking legal redressal at higher courts, the trial court is going ahead with its proceedings in which they are facing trial in the murder case of their teenaged daughter Aarushi and domestic help Hemraj.
The trial court had dismissed their petition on May 6 and ordered recording of statements of Rajesh and Nupur, who are the main accused. The statement of CBI Investigating Officer AGL Kaul, the last prosecution witness, has already been recorded.
The CBI case is that the murder of 14-year-old Aarushi five years ago was carried out by her parents and that no outsider was present.
In his deposition before the special court, Kaul, who headed the CBI probe, had submitted that the agency's investigation had revealed no evidence of any third person's entry into the Talwar residence.
Aarushi was found dead with her throat slit in her bedroom on May 16, 2008. The initial suspicion went on Hemraj whose body was later found in the terrace at their residence in Jalvayu Vihar in Noida on the outskirts of Delhi.