Sai's whereabouts are not known yet; the police had earlier issued a look-out notice for him.
"We have moved a local court for anticipatory bail for Narayan Sai in connection with the sexual assault case lodged against him in Jehangirpura police station," his lawyer Kalpesh Desai told PTI.
The application, which may be heard next week, questions the delay in filing of the first information report and alleges that the complaint is bogus. The Surat police recently registered two cases -- one against Asaram and another against his son -- of rape, sexual assault, illegal confinement and other offences upon the complaint filed by two sisters.
While the elder sister has accused Asaram of repeated sexual assault when she was living at his Ahmedabad ashram during 1997 to 2006, the younger sister has accused Narayan
Sai of same offence when she was living at Asaram's ashram at Surat between 2002 and 2005.
Seventy-two-year-old Asaram and his son have already moved the Gujarat high court to get the complaints quashed.
Asaram was arrested in August on the charge of sexually assaulting a minor girl at Jodhpur, and has been in prison there since then.
Jodhpur court allows Guj cops custody of Asaram
Asaram, son move HC seeking quashing of sexual assault plaints
AP: Employees call off stir; power stations resume operation
Two minor sisters raped in moving van for 2 weeks; 2 arrested
I will not run away, says Asaram's absconding son in ads