Crossbench senator David Leyonhjelm has declared the quoll should replace the domestic cat in an effort to preserve native mammal populations.

In a speech to Parliament the Liberal Democratic Party senator argued making it legal to domesticate native animals like the quoll and bilby would ensure their survival.

"Certain kinds of wallabies make great pets. The quoll may replace domestic cats," he told the Senate.

"The bilby is often nominated as a great candidate for domestication.

"In the right circumstances, possums, Tasmanian devils, wombats, native rats, antechinus and bandicoots would also be great pets."

Senator Leyonhjelm said 11 per cent of Australia's native mammals were listed as extinct and the nation needed to be better at preserving fauna.

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"Just as cats and dogs are in no danger of dying out, the same will be true if native animals are privately owned. It means they have value."

Senator Leyonhjelm also acknowledged it would not be appropriate in some cases.

"There is no disputing that some native animals may make unsuitable pets, at least in certain situations," he said.

"Many are nocturnal, for example, which might require us to adjust our own sleeping habits to enjoy them."

He cited examples overseas of sugar gliders and blue tongue lizards living longer in captivity than the wild.

Senator Leyonhjelm said the native animals would "need to be bred as pets".

He also noted that Australians can legally own a number of pets that kill native animals.

Greens environment spokesperson Senator Larissa Waters said Senator Leyonhjelm's suggestion was an attack on national parks.

"Suggesting that we can stop the our extinction crisis by keeping native animals as pets, while dismissing national parks flies in the face of the scientific evidence," she said.

"The suggestion that the only way to save native wildlife is to domesticate it is ludicrous."

Senator Leyonhjelm has previously revealed himself to be an animal lover.

Last week a photo tweeted by an advisor of Senator Leyonhjelm cuddling his white cat proved a hit on social media.