Yes, but it is not reccomended. Eachgame.hk, sells the casing for the Xbox 360 slim drive.
The Xbox 360 hard drive is a standard laptop 2.5 inch sata drive.
You would need to remove the hard drive from the original xbox styled casing. (which does require alot of effort. because one wrong move and the drive can be cracked from too much pressure on the lid.)
But if you wish to use your old drive. go that way.
KEEP IN MIND-
The Case, IS not an original Microsoft part.
So any Attempt to do so, Will Void any warranty regarding your hard drive if it fails.
Certified Computer Engineer, and Owner of own business for 5 years now.