Sai's whereabouts are not known yet; police had earlier issued a look-out notice for him.
"We have moved a local court here 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 FIR and alleges that the complaint is bogus.
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.
72-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.