I wouldn't suggest it because when that linoleum expands etc, it will crack your grout and tile. Best to take the extra step to rip up the linoleum and lay the ceramic tile (using the proper prep) over the sub-floor. You'll need to make sure your sub-floor is in ok shape, before laying the tile down.
My first choice would be to take it up, but you could leave it where it is, IF it is secure and has no "play" in it when you walk on it. When the floor is secure, you could screw down "backer board" and tile over it. The other issue you have to look at is...if you keep the linoleum will the new floor over it be to tall to get the stove and dishwasher out if it needs to be replaced. We are doing this same thing in our kitchen..... we had to take up two layers of linoleum and a rotted board between the layers because the moisture had gotten into it. Good luck!
@Cyndi Moore Tippett Yikes! You guys went through some sweat! Aren't reno's grand? LOL! We just ripped the crappy stuff up. Subfloor was good, so we are painting it and laying new lino in the center, to mimic a rug.
Monica.... definitely remove the existing floor and to install the tile properly......install an approved underlayment such as concrete backer board or hardi board underlayment. This will insure a stable surface for the ceramic tile with no future problems. Do not install the tile directly to the wood subfloor.....you will eventually have problems,