Microsoft’s Program Manager, Casey Penk answered to the uservoice suggestion for offline access on OneDrive that this feature would be added to OneDrive in future but, no exact release date has been provided.
This feature would be very useful for people who want to keep the files stored on OneDrive, offline for quick access while no internet connection is available. Offline access for Windows Phone will also be useful for pictures stored on the cloud drive where the same can be access on phone.
It would be interesting to see the selective file sync from Windows 10 coming to OneDrive since, syncing whole OneDrive to your phone won’t be possible due to limited storage.
Are you looking forward to use the offline access for files on OneDrive using your Windows Phone?
Source: OneDrive uservoice