The actors started working on Friday on the film, by Italian director Paolo Sorrentino, who is following up on his Oscar-winning flick The Great Beauty, Zurich-based newspaper Blick said.
Caine, 80, Fonda, 76, and Keitel, 74, are starring in the film, along with Rachel Weisz, 44, the wife of James Bond star Daniel Craig, and Paul Dano, 29.
The film, written by Sorrentino, is about two old friends on holiday in a luxury hotel in the Swiss Alps.
One is a movie director trying to complete his last film, the other is a long retired composer-conductor who is being encouraged to take up the baton again.
Fonda plays the wife of one of the seniors, while Weisz plays the daughter of one of them, Blick said.
The film is being co-produced by Zurich’s C-Films, Bis Films, Number 9 Films and French-based Pathé International.
Blick said scenes for the film are being shot in the mountain resort towns of Davos and Flims over the next several weeks.
“We are hoping that this will be a significant image boost for the entire region,” Marion Minarik, from the Hotel Waldhaus in Flims, is quoted as saying by Blick.
The luxury belle époque hotel is part of a hotel resort and spa centre in the Flims-Laax region.
Meanwhile, Blick reported that co-producer C-Films is looking for extras for the film — 15 “pretty women” aged from 25 to 34.
Those interested should email “full body shot” and portrait photos of themselves to firstname.lastname@example.org, using the subject tag “Paolo Sorrentino call”.