Cats, as we know, sleep anywhere. They'd prefer it if their 'bed' was something you actually had to use and might want not to have covered in fur, so tend to avoid anything originally built for the purpose, so the best way to trick them is to turn one of your old, once-useful items into a bed for them - and then they'll think they win.
I absolutely adore this idea for an old suitcase, and think it makes an excellent bed for a cat who wants to hog your things. Just look at the smug expression on this ginger boy's face. And the portraits on the 'wall' of the bed are such an adorable touch. The method for making one of these is here
Related: Recycled computer monitor cat bed | How to felt your own cat or dog basket
