Ampere's law - 2 current carrying wires

There is nothing in principle to prevent them from touching, but if they do it would likely create a short circuit.

Indeed this used to happen in earlier times when generating magnetic fields inside coils using large currents: the currents in neighboring turns of the coil would attract the wires and produce a “crushing” force that would eventually physically wear out the cladding around the wires through friction, with explosive effects. Regrettably I could not find an example of such an explosion on YouTube or similar sites but depending on the size of the coils the result could be quite dangerous.