"We seek permission to interrogate the accused in jail for three weeks," CBI special prosecutor Kavita Patil told the court.
Special Judge H S Mahajan is likely to hear the probe agency's plea on Monday.
On November 20, a Metropolitan Magistrate court had transferred the trial in the case to a sessions court here and had directed that the three accused be produced there on December 3.
"Accused Indrani, Khanna and Rai are further required to be examined in respect of the contents of messages exchanged over Skype between Indrani-Rai and Indrani-Khanna immediately before the incident. These messages have been retrieved by the forensic laboratory and the report has been received recently," said CBI in its application.
Meanwhile, Indrani, through her lawyer, moved an application seeking statements of witnesses recorded before the court.
43-year-old has Indrani also sought Rai's confessional statement in the case. The court will hear this application too on Monday.
Five witnesses have recorded their statements in the case under the provisions of section 164 of Criminal Procedure code, which unlike police statements, are admissible in the courts.
Indrani, Khanna and Rai were chargesheeted after their arrest in the case in August this year. Indrani's husband and former media baron Peter Mukerjea is in judicial custody till December 14.
He was arrested on November 19 and was subsequently subjected to sustained grilling and polygraph test during his 11-day CBI custody.
Sheena (24), Indrani's daughter from an earlier relationship, was allegedly strangled in a car and then her body burnt and dumped in a forest in Raigad, about 84 kms from Mumbai.
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