The fresh bail application filed by the three stated that there was no case made against them.
The court has asked the police to file details tomorrow and then the bail application will be heard.
A local court yesterday remanded Tarannum and two alleged bookies arrested on September 16 for their alleged involvement in cricket betting racket to judicial custody till October 10.
Tarannum and the other two Pradip Parmar and Milind Dhiraj Nandu have been booked under the stringent Information Technology Act, apart from charges of gambling and criminal conspiracy.
Tarannum, who in a television interview had repeatedly admitted of having indulged in betting, was under police scanner for her alleged proximity to some Sri Lankan cricketers and investigators are finding out if she had links in match-fixing.
After their arrest on September 16, the three were remanded to 10 days police custody.
Tarannum hit the headlines following an income tax raid that revealed large cash and property investment details.
Police took over the probe after Income Tax men found telephone numbers of bookies and some Sri Lankan cricketers in her mobile that subsequently led Tarannum to admit that she was associated with betting business.