Failure to do so before the law takes effect on July 1 could force the clinic to shut down.
The Clarion-Ledger reports that lawmakers who supported the measure have said they hoped it would close the Jackson Women's Health Organization clinic by creating abortion regulations the clinic could not meet.
The clinic's three abortion providers are obstetrician gynecologists. Clinic spokeswoman says that if the three are denied hospital privileges, the new law will be challenged in court.
Clinic officials have applied at every eligible medical center in the Jackson metropolitan and surrounding areas, Thompson said.
Admitting privileges at local hospitals may be difficult to obtain. Many religious-affiliated hospitals do not allow abortions to be performed at their facilities and some will not affiliate with doctors who perform abortions at other hospitals or clinics.
Public hospitals like the University of Mississippi Medical Center have strict guidelines. At UMC, doctors must apply with the appropriate clinical department, where officials determine whether applicants meet basic qualifications, spokesman Tom Fortner said. Then, the executive committee of the medical staff and the dean of medicine must approve the application.
Republican lawmakers who supported the law were banking on abortion providers having difficulty obtaining admitting privileges at local hospitals.
"If we require them to have admitting privileges, and the hospitals don't provide them, and I don't think they will, then we can end abortion in Mississippi," Lt. Gov. Tate Reeves said during the recent legislative session. "That should be our No. 1 priority."