Flooring Tile - Wish to tile on SLAB, with sloping floor to drain

Great forum ... VERY informative, so thanks.

I'm looking to tile my (currently linoleum) kitchen/dining room floor. However, my house is on a slab and there is a drain in a utility closet (with the water heater & furnace/heat pump - imagine the drain in a basement floor, this is just like it) just off the dining room.

The floor in the dining area slopes toward the drain located in that closet I described. I understand I could use a self-leveler to level out the slope a bit, but I don't want to defeat the purpose of the slope. Afterall, it's there for a reason, and if there were ever a disaster in the kitchen (dishwasher malfunction, broken water pipe, ice maker leak, etc.), I'd hate for the place to flood because I leveled out the floor so I could lay down tile.

Has anyone ever encountered this? I figure vinyl tile would be much more compatible with a sloped floor, since it is flexible.

Any input would be greatly appreciated. Thanks in advance!

Ceramic tile could be easily done as well...it's done all the time.:)

Don't use large format tile. 6x6 or 4x4 tiles. For really concave surfaces, 2x2 mosaic, The smaller the tiles the more bending it does without noticeable lipage.