No, but there is a third party FPGA core available which is called 68080, it's used in a modern line of Amiga accelerators and clones.

Not Motorola (or Freescale). After the 68060 they dumped the mc68k architecture outside the embedded market (68300 line) for the 88000 RISC architecture. After 2-ish generations of 88k, they dumped it for PPC.

There are numerous FPGA implementations of various folks ideas of what a post-060 mc68k might look like. There's also a 68070 from Philips that's a 68000+simple MMU+stuff; definitely not 060 class.