Computer to computer backup

I would like to backup my laptop files useing norton backup to an external drive on a different computer Desk top. Is that possiable? I have shared both drives on both computers. Both are win 7 the laptop is 32bit and the desktop is 64bit. I have Norton 360 running on both computers  and the desk top is already backing up to the external drive. When I access Norton backup on the laptop I don't see the shared drive of the desk top as an option for storage of the information. Just don't want to have to carry computers or drives from place to place. Figured if I could access files and change them then save them from computer to computer I should be able to access and back up to the external drive as well. Would apprecieate the help! Thanks in advance.