By tile, I assume you mean ceramic? I <have> seen it done with mastic over
linoleum on a plywood subfloor, but even if the old linoleum is stuck firm,
I'd be paranoid about the thinset or whatever sticking to a surface designed
not to have stuff stick to it. I'm sure the experts will jump in here, but
I'd also wonder about having what is essentially a vapor barrier in the
middle of two quasi-stone materials. They rent machines to pull up linoleum-
stinks like hell and puts off nasty fumes, but it does get the stuff up.
Recommend asking your tile manufacturer/vendor, or your installer (if you
were gonna use one) about acceptable substrates. YMMV, of course, but to me
personally this would fall into the category of hiring someone who has done
the work before.
I lay ceramic tile over vinyl/linoleum floors all the time with no problems.
I also used to work for a builder who laid vinyl first before tiling to keep
the tile from cracking. He cut his tile call backs by 97%.
Having said that the vinyl or linoleum must be tight to the floor.
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