Combine Duplo feet with regular LEGO
I am still waiting for the bricklink delivery with 27448 tiles that Alex suggested in one comment of his answer. Therefore, I tried a less subtle solution:

This is the starting point: A DUPLO pig that needs to be put directly on LEGO pieces.


I decided to cut a DUPLO piece to regular LEGO size. A DUPLO 2x2 brick was converted to a ...


... 4x4 tile, modified, with 2x2 DUPLO studs. My methods were crude (metal saw and cutter), but it worked quite well. There is only little height difference to the surrounding LEGO plates, and the clutch power is really good:


This is an approximation of the final goal to use the DUPLO pig as a figurehead in a LEGO MOC/MOD:


Edit: The 27448 tiles finally arrived, but there was no way I could get clutch power. I measured 9.3 mm for the diameter of the tile ring, and 9.4 mm for the DUPLO stud. This difference is enough to loose any clutch power. Even with 4 tiles combined there was no binding strength at all. Other DUPLO animals showed same results. A DUPLO human figure, however, could at least have a little bit of bonding when the ring is pushed into the toe area.