The first problem is that the new tiles will not stick well over the vinyl. Vinyl has a top layer of plastic which, since it is a slick surface, will not give the porousness necessary for the tiles to stick well, not matter what kind of glue you use. Some people think they will get around this by roughing up and sanding the surface to make it adhere better, but this will not make a big difference. Since the tiles are not going to stick to the underfloor, they will eventually lift, and you will have to replace parts or maybe even the entire floor. No time saved there.

The second problem is that you will not have a level surface. To make sure your floor is completely level is hard enough when you are working with a new sub floor, but if you have vinyl with varying heights of adhesive under it, it is next to impossible.

The third problem is the surface under the floor may not be the right kind for tiles. Vinyl can be installed over 1/4" plywood or particle board, but these are not approved surfaces for tile. If you put the tiles over the vinyl on these surfaces, you will end up with a floor that moves and can therefore crack and lift easily. If you get this kind of lift or flex, you will have to replace the floor since replacing one tile is very difficult. First of all, lifting it out without damage to the other tiles is not easy, and after your tiles have been down a while, you will not be able to match them perfectly.

If you insist on leaving the vinyl down, you have to do a completely different kind of preparation for the floor. You have to screw down the vinyl and cover it with a mortar base using mesh and concrete. If you don't want to deal with concrete, you will have to put a new sub floor down over the vinyl. Some new products are out now that will help avoid cracks in tiles that are laid on wooden sub floors. But all of these work seems harder than just lifting the vinyl, so why not just do that? In addition, the problems of lifting and unevenness will not only be unattractive, they may also be dangerous.

If you absolutely have to leave the vinyl down, you should have a professional tile installer look over the job. They will discuss your all of you options and help you decide. Moreover, a professional will also advise you about the best brand of the tile to buy and may be even suggest dealers from where you can get the product at discounted prices.