Rowan County Clerk Kim Davis, who come to national attention when she refused to issue marriage licenses to same-sex couples because of her Apostolic Christian beliefs, claims she will not violate her conscience when she returns to work.

Davis's lawyer, Mathew Staver of the Liberty Counsel religious freedom organization, hinted on Sunday at a possible resolution to a legal standoff between the clerk and the courts, saying Davis would be willing to process and file licenses if they did not bear her name.

RELATED: Kentucky clerk's office issues marriage license to gay couple, ending ban

"She is asking for something very simple, and that is just to accommodate her by removing her name and title off these certificates," Staver said on CNN on Sunday. He said Kentucky's governor had authority to change the licenses.

In her absence, deputy clerks have been issuing licenses and have said they would continue to do so.

RELATED: Kentucky clerk defies Supreme Court, still denies gay marriage licenses

The issuance of marriage licenses to same-sex couples in Kentucky and other states has become the latest focal point in the long-running debate over gay marriage that has continued after a U.S. Supreme Court ruling in June that extended the practice across the United States.