According to Variety, the two actors have joined Bahrani's upcoming project about a farmer whose insistence on manic expansion leads to issues with his sons and wife.
Few details about the currently untitled project are known, although it is expected that Quaid will play the lead role of the farmer.
Quaid recently starred in the drama Soul Surfer and will be seen in the remake of Footloose as Reverend Shaw Moore later this year, while Efron is currently filming a supporting role in the romantic comedy New Year's Eve.
Bahrani has been acclaimed by critics for his independent films, including Man Push Cart in 2005 and Chop Shop in 2007.
London-based production studio Bandside Films are pitching the project at the Cannes Film Festival this weekend.