The plea was mentioned before a vacation bench of Justices A M Sapre and Ashok Bhushan who fixed the matter for hearing on May 30.
Counsel appearing for Pratyusha's mother Soma Banerjee said Rahul should be taken into custody as the investigation is still on in the case and there is likelihood that evidence could be tampered by him.
In the petition filed before the apex court, her mother sought custodial interrogation of Rahul contending that there were several deep injury marks on the body of the deceased.
The High Court had on April 25 granted anticipatory bail to Rahul who has denied the allegations levelled against him.
The police had earlier filed a report before the High Court in which it had alleged that Rahul, who was staying with Pratyusha at a flat in Goregaon in Mumbai, used to assault her and borrow money from her.
The 'Balika Badhu' fame actress was found hanging at her residence in Goregaon on April 1 and was rushed to a hospital by Rahul in Andheri where she was declared dead.