In the past few months, Microsoft has introduced a number of new features and visual tweaks for OneDrive for Windows Phone, but there's no offline access available, although it's present in the desktop version. However, users who are waiting for this feature may get their wish fulfilled soon.
In response to a user on OneDrive UserVoice, Microsoft's Program Manager Casey Penk said the company "intend(s)" to bring this feature, but at the moment, they don't have any estimated time frame available.
We know offline access is important, and we intend to bring this feature to Windows Phone. We don’t have a specific timeline yet.
We can't be sure when Windows Phone users will be able to enjoy this feature, but we'll definitely update you as soon as its available.