Rogue Liberal MP Sussan Ley insists she's entitled to push for an end to live sheep exports, despite the prime minister trying to talk her out of it.

The former cabinet minister intends to introduce a private member's bill to phase out the trade which is under increasing pressure following revelations of animal cruelty on ships bound for the Middle East.

Shocking footage prompted Agriculture Minister David Littleproud to commission a series of reviews, including a veterinarian-led audit of the northern summer trade, which is expected to deliver its findings late next week.

Ms Ley denied her conversation with Malcolm Turnbull was fiery, saying the Liberal Party had a tradition of MPs standing up for their beliefs.

"It's the prime minister's job to promote government policy and argue the case for waiting for the review and seeing what comes out of the minister's very positive actions so far," she told Sky News on Thursday.

"I'm entitled as a private member to lodge this bill and argue for my case."

Ms Ley, whose electorate is in country NSW, said she had overwhelmingly positive feedback.

"One sheep farmer rang up and said the truck was loaded and about to leave his property," she said.

"He asked where the sheep were going, was told they were going to the boat and said: 'You can unload them right now'."

Former Nationals leader Barnaby Joyce said Ms Ley was on the wrong path, with the 2011 suspension of live cattle exports a reason why a ban should be opposed.

Mr Littleproud told radio 5AA live exports moving to onshore meat processing was a definite possibility, but any shift would be decades away.

In the meantime, he's concentrating on improving animal welfare standards and punishing exporters who do the wrong thing.

"We've got to be pragmatic and understand that there are nations around the world that don't have the cold storage facilities that we do," Mr Littleproud said.

"They need to take live animals to feed their nations."

Meanwhile, the Greens and independent senator Derryn Hinch postponed introducing their own bill to end live exports until the next sitting of the upper house in June.

"There's two or three Libs that are very keen to cross the floor," Senator Hinch told Sky News.

Senator Hinch, who has campaigned to end live exports for 37 years, believes he's closer than ever to shutting down the trade.