The convent, which was once home to Sisters of the Immaculate Heart of Mary, is being sold by the Archdiocese of Los Angeles for a reported £9.6 million.
But two nuns have said it should not be sold to the world famous star and doing so would 'violate' their pledge to the Catholic Church.
In an email to the Archdiocese they said: "In selling to Katy Perry, we feel we are being forced to violate our canonical vows to the Catholic Church,"
The sale to Katy Perry, whose mother and father are pastors running a ministry in the US, was approved by the Archdiocese recently.
The nuns are arguing that the property, with a sweeping view of California's San Gabriel Mountains, is theirs and only they have the right to sell it.
They claimed to have agreed terms with restaurateur Dana Hollister.
Perry, singer of hits such as I Kissed A Girl, Hot & Cold and Roar, met the nuns in May to attempt to convince them to approve the sale.
It's reported she sang the gospel hymn Oh, Happy Day and showed the sisters a tattoo of the word 'Jesus'.
Sister Rita Callanan told the Los Angeles Times she searched the internet for Miss Perry: "I found her videos. I wasn't happy with any of it."