I definitely believe it's possible, maybe even likely, that leopards and cougars have been seen roaming wild in Australia. But it definitely isn't a "thing" i.e. wild populations of these great cats. I think the vast majority of sightings are simply feral cats. I've done field work in Western Australia in which a 6kg immature female cat was trapped and weighed. Doesn't sound huge, but that's a female that is likely to grow 2-3kg heavier than your average domestic tomcat, in an area not notorious for producing big feral cats. Colleagues have also described to me cats a whole lot bigger than this, possibly heading towards the 15kg region (the weight of a Kelpie, for reference).
It seems NT has been finding some big ones too- http://www.abc.net.au/news/2013-06-04/huge-feral-cats-arnhem-land/4731696
You can also pretty much rule out interbreeding forming a hybrid population of larger than normal cats. Leopards you can definitely rule out; if not on size alone, leopards are a member of the subfamily Pantherinae, where as domestic cats are in Felinae. Cougars are also in Felinae, and although I've forgot almost everything I learned in my Genetics units, I'm fairly sure they are too distantly related to reproduce together. Just to contradict myself and leave it open for discussion, Cougars and Leopards can interbreed and produce offspring, and Cougars have interbred with the much smaller Ocelot, which in turn can interbreed with Domestic Cats.
It seems NT has been finding some big ones too- http://www.abc.net.au/news/2013-06-04/huge-feral-cats-arnhem-land/4731696
You can also pretty much rule out interbreeding forming a hybrid population of larger than normal cats. Leopards you can definitely rule out; if not on size alone, leopards are a member of the subfamily Pantherinae, where as domestic cats are in Felinae. Cougars are also in Felinae, and although I've forgot almost everything I learned in my Genetics units, I'm fairly sure they are too distantly related to reproduce together. Just to contradict myself and leave it open for discussion, Cougars and Leopards can interbreed and produce offspring, and Cougars have interbred with the much smaller Ocelot, which in turn can interbreed with Domestic Cats.