Well, yes, in your case with certain assumptions, you can install over the vinyl. HOWEVER, you will need to install a cement backer-board that's AT LEAST 1/2" in thickness. The thickness of this board will depend on what additional 'layers' of flooring/subflooring you have. If you've removed 'scraps' of tile, you'll need a floor leveling compound to 'fill in' the missing pieces. YOu need to do this because the floor needs to be FLAT and level. If you don't fill them in, your backerboard may 'flex', and the next thing you know, you'll be asking 'us' why your grout is cracking or your tiles are coming loose. Bottom line - The flooring that's installed BEFORE the tile goes down MUST be 'tight' and non-moving.
Of course, I'm assuming you're not dealing w/a concrete slab (in which case the floor won't flex BUT you still need to fill in any 'gaps'.) There are plenty of books and pamphlets out there in doing this job. Consider contacting the MFGR. of the ceramic to see if there's free information for you. Be SURE to read the Warranty too because if you deviate from it, you won't be covered.