Perry, 30, has her sights set on an eight-acre estate in Los Feliz, but two sisters oppose the idea of their former convent, where their mother house had been based since 1970 falling into the hands of the pop star, according to the Hollywood Reporter.
Sister Rita Callanan and Sister Catherine Rose Holzman are against the idea of Perry taking ownership and are in favour of selling it to Los Angeles restaurateur Dana Hollister, who is also vying to purchase the property.
The archdiocese has sued Hollister, and Judge Robert O'Brien has been asked to issue an injunction to stop Sister Rita and Sister Catherine Rose from selling the property to the restaurateur, who reportedly already has moved into the estate.
"There is no reason for them to allege that," Hollister has said of the claim. "It is part of the ridiculousness that propels this whole story forward."
A hearing will take place on July 30 in the Los Angeles County Superior Court.