The newspaper said Turner has already passed the civics exam and interview, the only things standing between her and a Swiss passport.
Turner, born Anna Mae Bullock in Nutbush, Tenn., moved to Kuesnacht, a suburb of Zurich, in 1995 with her longtime manager and romantic partner, German record executive Erwin Back, The Hollywood Reporter said Friday.
Jo Matherne, the mayor Brownsville, Tenn., which encompasses Nutbush, said she was surprised to hear the town's favorite daughter had decided to renounce her native country.
"I think anytime a person, whether they're world-renowned or the most meek and mild, makes the decision to change their citizenship, we need to step back and think what causes that decision," she said.
Turner's representative said she has no comment until she contacts Turner to clarify the matter, TMZ reported.
Turner's change in citizenship must be approved by Swiss federal officials before she is handed her new red passport, The Hollywood Reporter said.
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