Mediaworks has yet to respond to requests for comment but earlier today told The Herald it would not comment on reports that the show's future was in jeopardy, labelling them "speculation".
Questions about Story's fate were raised yesterday as news broke that high-profile broadcaster Paul Henry is set to step down from his role at the network. Garner is understood to be in line for Henry's morning news role.
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Henry has bought a property in Palm Springs, California, and wants to move to America, according to those close to him.
It is understood he has no interest in working full time in New Zealand broadcasting anymore but will continue to work on select television projects.
Sources say Henry has been unhappy for a long time and regularly complains about the early morning starts.
But attempts to coax the broadcaster to stay on have failed, according to sources, who say Henry will leave at the end of the year.
At the time of its announcement in June last year, Story was billed by TV3 as a "smart, fun and thought-provoking show that will lead the way in daily current affairs".
MediaWorks group head of news Mark Jennings, who has since left the network, said the duo would be "a formidable team".
"'I see this as a great chance to be part of a programme that will reflect our country and our lives - no matter where we live. I expect us to have fun, to laugh, to entertain and to tell your stories," Garner said.
Du Plessis-Allan, who was head hunted from TVNZ by TV3 for the role, said she was excited to be part of the show.
"Duncan is one of the best journalists around so I'm stoked to be able to learn from him," she said.