Shah, facing murder and extortion charges in the fake encounter case, was arrested yesterday and was sent to judicial custody till August 7 by special CBI magistrate A Y Dave.
According to the application filed in the CBI court here, the central agency wants to interrogated Shah inside the jail premises itself.
The hearing on this application is likely to take place later in the day.
46-year-old Shah, who resigned from the Modi government on Saturday after being chargesheeted by the CBI in the case, has denied all the charges against him.
The chargesheet has named Shah as a key accused along with IPS officers-D G Vanzara, Rajkumar Pandian, M N Dinesh and Abhay Chudasama. In all, 15 accused have been named.
According to the chargesheet, it was Shah who had entrusted the task of eliminating Sheikh, an alleged gangster, to Vanzara, Pandian and Chudasama.