Samsung is working on it, however, with plans for a device that simply folds in half and a new patent filing has showed up, indicating exactly how that might work.
The patent was filed in November last year, according to Patently Mobile, but was published only this week.
The Korean technology firm has long talked about its plans for a flexible, foldable smartphone over the years, however the technology has not quite kept up with aspirations.
Now developments in Oled screens could make a foldable screen reality, and sooner rather than later, with some analysts even predicting one within the next year.
Samsung's most recent flagship devices, including this year's S7, have inched closer to full foldability with curved screen edges. But the latest patent, which appears to look similar to the Galaxy models, would indicate a major step forward.
Smartphone sales have started to slow and device makers are finding it increasingly difficult to differentiate their products from rivals with new features. If Samsung were able to get the foldable smartphone into production - rumour has it this could be the Galaxy X, which is known by its code name Project Valley - it would be a first that could set the firm apart from its competition.