The design features an innovative hinge mechanism that would prevent creasing issues similar devices have suffered from.
Movable flaps would prevent unsightly marks by keeping the device in a semi-curved state when shut.
Huawei, Samsung and Lenovo were among those to release foldable devices in 2019, to varying levels of success.
“Apple has a long history of assessing technology and only jumping into the market when it feels a particular technology is mature enough or that it can use it in a way that makes a meaningful difference to its products,” said analyst Ben Wood.
“There is little doubt Apple has probably been assessing flexible displays for years behind closed door and it comes as no surprise it is trying to do something different.”
It marks the latest in a series of patent filings by Apple over the past five years related to foldable devices.