If so this is possible, If sheet, you have a problem and I would suggest to change to square vinyl lino.
You have only two choices to cut around the feet. Get a piece of heavy cardboard and cut in and around the feet and translate this to a vinyl square. Then finish out with caulking.
Second, if you like to walk on the wild side, you can get a small jack, sissor type, with some buffers and jack up the tup about 1/4 inch. Then remove the old and just place the new in the slot. normally 1/8 inch is all you need and in MOST cases will not damage the plumbing at all. Do only one leg at a time. The back legs actually may go the 1/4 inch, but the front may not go that much safely.
Personnally, I would suggest to cut around the claw feet.