Unless you want to add a bit of de and re construction to this project the barn door type would be the only sliding option i can think of.
Add a door to a room.
To preserve the cripple studs calculate where to cut them by adding the jamb height included in the packaging for pre hung doors and the header size calculated below plus inch wiggle room.
Add your door handle to the door.
4 measure the width of the interior pre hung door and add 3 inches to the measurement.
Nail three pieces of 1 1 boards into the cased opening on the opposite side of the door swing to hide your gaps and keep the door from swinging too far inside the frame.
The first step is to select the new door you plan.
Remove the plaster or drywall to this point and cut a straight line across the studs you want to save.
I used this oil rubbed bronze privacy lever door handle.